Part 1/2.

Yes, I know of at least 2 such instances.

The Battle of Kolberger Heide 1 July1644 in Kiel bay between Swedish (34 ships, 7 burners) and Danish (40ships) forces. This took place during the overarching 30 Year War conflict in what Swedish history knows as Torstenson's War 1643-45 (after the leading Swedish commander ). The main reason for the war was basically that it was opportune for the Swedish. The Danish king had earlier in the 30YW conflict intervened in his role as Imperial prince (i.e. Denmark itself was technically not at war with the Emperor) and largely financed by the king's control of the Öresund toll and Dutch and English subsidies. The intervention 1625-29 had ended badly for the Danish and their mostly German mercenaries ranged against both Tilly and Wallenstein, and a peace was agreed with the Emperor knocking Denmark out of the conflict, a fairly benign peace at that as the Emperor could afford to be generous.

Incidentally this intervention and it's failure encouraged the Swedish intervention and the dismissal of the Danish king's mercenaries provided the incoming Swedes with a nucleus of a ready made experienced army. The Swedes ran rampant over German lands until the king's death in 1632 and fortunes billowed back and forwards ever after. By 1644, finally bolstered by regular French contributions, the protestants in Germany headed by Sweden and France were slowly tipping the balance over, fighting was now more concentrated to south and middle German lands.

With the French deploying armies of their own the Swedish chancellor Oxenstierna (think Richelieu, but nobility, not a churchman and you aren't far off) decided the moment had come to settle the score with the Danes. Why you ask? They were all protestants and sorta kinda allies in Germany right? Not exactly. The Danish king had originally intervened in part to grab the mantle of protestant head-honcho so the Swedish king wouldn't. Sweden was ascendant and this could not be tolerated in Denmark, who consequently schemed at every opportunity to worsen the Swedish position. The Swedes well well aware that Denmark had sought alliance with the Emperor, Poland and Russia, all current or traditional enemies. Denmark had territory allowing armies to easily springboard into Swedish territory and Sweden had likewise for years tried to encircle Denmark with allies or potential German footholds to attack them. The Öresund toll was a constant irritant and the Swedish feared (not unjustified) that it would soon finance operations against them. Basically Swedish operations in the 30YWoperated with a strategic weakness at their back of a Denmark always willing to fall on it if it showed weakness.

Thus, the Swedish chancellor figured with money and armies available at the time, a strategic threat could be removed. It also shouldn't be underestimated that one of the unfortunate logics of 17th century war was that it was better to be at war and feed off enemy lands than support your own army, and since they could not disband the army due to the unresolved if quieter conflict the army needed a war. The surprised Danish could only watch (well they did fight as best they could) as the veteran Swedish army rolled over Jylland (the part connected to the continent) and the Scanian lands, though could not easily access the sea. For Denmark's survival it was important that the Swedes could not take their fleet to the Danish isles and ship the army over. This is where the battle of Kolberger Heide fits in. The Swedish fleet lay at anchor near Fehmarn island when the Danish fleet found them.

Among the leaders of the fleet was the king Kristian IV. He had admittedly delegated top command to the riksamiral (sort of 1st lord of admiralty) Jörgen Vind, an experienced naval commander. This was the first time the Danish and Swedish fleets had met in 70 years. And it was one of the first naval battles where the commanding officers led the fleets even after the engagement started and the fight was conducted mainly by shipboard artillery. The reason I chose to list this as an example is because king Kristian IV was wounded and lost his right eye in the battle and you gotta respect that. It inspired the national and royal anthem "king Kristian stood by the lofty mast" so IMO significant there too.

The battle itself was a draw, almost bloodless and no ships lost, but a great tactical and strategic win for the Danes who could bottle up the Swedish navy in the bay of Kiel and thus neutralise it for awhile and stop a combined invasion of the main central Danish islands and allowing the Danish to push back in the Scanian side of the war. Unfortunately for the Danish the Swedish fleet eventually managed to slip out after a month. The Danish king also led other naval battles like Lister Dyb that he won against the Dutch who had arrived to assist the Swedish.

As a direct consequence the battle of Femern took place in October 1644 with combined Swedish-Dutch and the Danish fleet again with the king in significant command. This ended up as one of the greatest triumphs of the Swedish navy ever and effectively eradicated the Danish navy. With a loss of naval control of the waters around Denmark, hostile armies inside his territory and more available the Danish king had no choice but to negotiate a hard peace of Brömsebro in 1645 losing Jämtland, Härjedalen, Gotland, the island of Ösel and finally Halland for 30years. More woes would come for Denmark in the following years and that 30 years would turn to forever and all of their remaining holdings in what today is Sweden would be lost in the years to come. The Danish were on the decline and Sweden was on the up.

to be continued...

Part 2/2 (not sure how reddit sorts this on my screen it's the wrong way around)

The other example is Swedish funnily enough. It's that viking blood I guess. When we stopped off last time Sweden was on the up. By now it's on the down. Way down.

The (second) battle of Svensksund in 1790 between Sweden and Russia.

There was also a first one in 1789 between the same parties where the king was also present where the much outnumbered Swedish fleet was badly mauled but managed to escape allowing it to return the next year with a vengeance. The background is as follows...

In 1772 the Swedish king Gustav III ended the "time of liberty". A period of time after the Great Northern War that had ended the Carolinian absolutist rule with the death of Karl XII, with a set of weak, constitutionally limited (foreign) kings where Sweden effectively became republic of nobles in all but name. The power passed between two loose groups of nobles, the "hats" and the "night caps", roughly analogous to Whigs and Tories though not necessarily in all their political ideas. Suffice to say they usually opposed what the other party wanted in parliament and whoever managed to get on-top ran the royal council and thus effectively the government.

Gustav III decided to be more like his namesake (the warrior-king Gustav II Adolf) and managed a coup-d'etat in 1772 and pushed through legislation in parliament in 1789 (with the help of the 3 not-noble estates who were rather fed up with the nobility pushing them around) that effectively gave him back absolutist powers. In the years leading up to the war there was internal issues and famine, so a uniting external war looked appealing and Russia was actually a guarantor for the pre 1772 constitution which might give them cause to intervene at an inopportune moment. The alliances against Sweden were at the time in disarray and Russia, by now the main Swedish opponent and strategic threat, were occupied by war against Turkey and would thus be unable to focus it's power on Sweden. Now the king needed a casus belli.

Not without reason is he known as the theatre king, so he dressed up troops in Russian uniform and had them perform a false-flag operation. I'll admit this is something usually taught to everyone in school, so it might actually be somewhat apocryphal, but it would fit his temperament, though the claims seems to be sourced I've not seen the primary source myself. Either way he declared war on what one must assume was fairly surprised Catherine the Great. Symptomatic of most wars after the early 1700s it went fairly badly for the Swedish army, the troops were not enthusiastic, the Finnish officers did not believe in the causes and supply was problematic. A group of officers even wrote a note to Catherine the Great asking for peace. The one bright spot at the beginning was Denmark declaring war. As the king himself reportedly exclaimed "I am saved!". He had a reason to distance himself from the failing war and support for the war increased with both arch-enemies engaged and the officers looked positively traitorous in light of developments. Even though the Danish intervention was half-hearted and didn't really lead anywhere.

By 1790 therefore many things were looking bad and the Swedish desperately needed an out. Enter the Archipelago Fleet, or more properly, the Fleet of the Army. This was a special brownwater (if our cold, crisp and clear blue coastal waters were brown, none of you have heard of algae blooms right? no? good, clear and blue, I swear) navy of sorts, consisting of galleys and smaller roundships specially designed to be shallow-drafted to be able to operate in the coastal region of Finland where, basically, traditional ships of the line could not go. If they value their hulls not being torn up running aground in shallow and narrow waterways. And most bluewater naval captains prefer land a safe distance away. The Army's Fleet was part of the army (if the hats got to decide at any rate, the caps put them under navy jurisdiction, see told ya, opposite views) and integrally working with ships and troops. I guess something like the marine corpse also works as a comparison. The purpose being specifically to defend the coastal region were the bluewater navy simply could not go. Together with coastal fortifications and naval bases this was one of the main defensive measures Sweden had. The access to inland roads was basically non-existent and most important things in Finland was (and is, fight me inlanders) concentrated to the coast. If you controlled the coast you controlled the area.

The plan since the start had been that the army supported by it's fleet would march towards St. Petersburg screened out at sea by the regular navy (which was still effectively able to contain their Russian counterparts). Swedish plans tend to go somewhat awry at the time though. Despite some successes July 3th 1790 found the king Gustav III, 30,000 soldiers, 47 ships of the navy, 174 ships of the Army of the Fleet and 60 transports blockaded in the bay of Viborg. Sweden faced the loss of most of the army, the entire navy and the king. The night of July 3th a favourable wind rose and the Swedish units fought their way out of the trap at some loss. The Fleet of the Army regrouped in Svensksund inlet. July 9th the Russian galley fleet caught up and initiated a battle to destroy their Swedish counterparts. The Swedish held a strong defensive position in the narrows, the Russian rowers were spent, winds were unfavourable and Russian leadership abysmal. King Gustav III led his fleet in a crushing victory with few losses, destroying 1/3 of the Russian fleet. This gave the Swedes a negotiating position and a status quo peace was signed soon after with Russia formally acknowledging return of full sovereignty. Seeing as they could thus conclude an unimportant conflict they hadn't started with no real loss the choice was easy.

The theatre king himself though? He paid the dividends of peace with the dissatisfaction he had stirred and was assassinated by a noble and officer plot in 1792. Ironically being shot during a masquerade ball in the royal theatre he had built. His bloody clothes from the night can still be seen exhibited in Stockholm.

In other fun connections the two constitutions of 1772 and 1789 Gustav III pushed through? They became the foundations for the the new Finnish "state" when Finland was lost to Russia in 1809 (and even independent Finland in 1917) and the wide powers granted was likely instrumental in convincing the then Tsar to keep them in effect. A fact that was skilfully used by later Finnish statesmen to avoid being easily integrated into the Russian empire and eventuality paving the way for independent Finland.

This is early in the "medieval" period, but adapted from an older answer of mine:

Adapted from an earlier answer:

What we know about naval warfare in and around Britain in, say, the period of the Norse invasions, is that ships were primarily used to move troops and their equipment around. There was no true naval warfare, if by naval warfare we mean warfare unconnected to war on land. Rather, ships were used to project power on the land, and the seas remained a debatable place. That meant that, on the one hand, there was little one could do to prevent an enemy landing troops on one's land, but on the other hand, one could equally as well count on using one's own ships and forces to force a landing on an enemy's coast. The scouting systems used at sea that would prevent that didn't develop before the 16th century or so.

When we see accounts of naval battles, they are universally fought inshore, usually in a bay, an estuary or even in larger rivers, and are usually fought as an auxiliary to a land warfare engagement. There were no missile weapons that could sink ships, and it wasn't possible to fit rams to the ships of the Norse and their imitators, so it was only inshore that grappling and hand-to-hand fighting could take place. Also, inshore communications were quick enough that they could on occasion call for help when a landing occurred, a prerequisite of getting ships together to fight.

Naval warfare in this era has been compared to mounted warfare on land: ships were a way to transport a group of raiders quickly to a destination and achieve strategic surprise. Shallow-draft ships could also carry raiders hundreds of miles into the interior of a country, using rivers for transport.

A scenario might be that a group of raiders has landed at a village, dragging their ships onto the strand, and that a counter-force manages to trap them with beached ships and burn their means of escape; the raiding force could then be hunted down on land. Many of the battles that we know about during this time period seem to take that form (the details of naval battle are very incomplete). Alternatively, there are some accounts of battles on the water between two fleets, where it seems likely that individual ships grappled with one another, with boarding being the decisive factor in their success. We do know that defense against ships in this era required a combination of fixed defenses (bridges, forts) and squadrons stationed at spots where they could quickly be called to respond. The accounts of battles that we do have tend to list a prince and his achievements (Alfred of Wessex went to sea with a "fleet" (sciphere) in 875, fought seven enemy ships and captured one ... etc.)

What we do know is that the type of ship used for warfare at sea in northern Europe was generally of the "longship" type, although the size varied by design. Ship-houses that have been excavated in Norway point to ships of maybe 80 feet long and only 15 wide, which accounts for them being called "longships" or "snakes." The size of those ships was measured in "rooms," being defined as the space between thwarts. The Skudelev 2 ship is a 25-room ship, about 100 feet long and 12.5 wide that would have carried probably 75-80 men (apologies for Wiki link).

Ships of less than 20 rooms don't seem to have been counted as warships, generally, and the size of a king's ships was bandied about in chronicles as a measure of his power. In the Norwegian fleet around the year 1000 or so, ships of 20-30 rooms were called "esnecca" or "snekkja," snakes, while those of 30 or more rooms were "drekkar," dragons, and considered quite unusual.

In terms of how Alfred was able to successfully defend against the Norse, fortified towns (burhs) were fortified locations, usually linked to settlements, linked by roads, that could command key fords or crossings; sometimes double-burhs linked by a bridge would bar passage along or across a river. Alfred teamed the burh system with a mobile army, mostly cavalry, that could quickly respond to attacks. It was similar to the system that Charles the Bald was developing in the Frankish empire, and one that Offa of Mercia had developed about a century before Alfred (Offa, though, lacked Alfred's purpose-built fleet).

The cavalry could alert nearby ships leading to small raids and ambushes that would occur when men had left their ships and their retreat was cut off by an arriving force. The Anglo-Saxon Chronicle has a description of such an action in 896, where a force of six Danish ships was raiding along the Isle of Wight. Alfred sent a force of nine ships to intercept them; when they found the Danes, three ships were beached with a small shipguard while the others were upriver raiding. The English ships attacked the guard ships and captured two of them, while one escaped, but in the process the English ships were grounded on an ebb tide, with only three of the ships on the same side as the rest of the Danish fleet and the other six on the other side. The Danes returned from raiding and attacked the three English ships, losing 120 men to 62 English killed. The battle ended when the rising tide re-floated the Danish ships before the bigger English ships, but only one escaped.

While there will always be more to be said, I posted some examples of the naval battle in which the (mainly Scandinavian) ruler led the fleet by himself in: Were the Vikings in any notable naval battles?

Even after the so-called Viking Age, the ruler/ king of Norway did not abandoned the tradition of to lead the expedition fleet by himself as well as join in the battle entirely, as I cite an stanza of the poem on the Battle of Menai Strait (Anglesey Sound) in 1098 between King Magnus Barefoot of Norway and the Norman Earls in: Were archers seen as cowardly by the vikings and other germanic as well as celtic cultures?. The battle itself also occurred on the shore, so I'm not 100% sure this battle should be classified as 'naval' one, though. King of Norway also led the expedition fleet by himself as for the case of the battle of Largs in 1263 against the king of the Scots (also briefly mentioned in my previous post, Has Norway invaded England since 1066), again the battlefield itself was on the shore (land), not in the sea.