Hi there, while you're right that 18th-century naval battles did not usually end with a large number of sinkings, it was not completely unknown. That said, though, the largest cause of the loss of ships during battle during this time was capture by the enemy.

If that was the case then how would you be able to verify that you are victorious?

Th main reason would be that you had beaten the enemy fleet into submission, forced it to flee, forced ships to surrender or disabled them completely. The fighting instructions issued to British captains generally contained some version of the phrase "take, sink, burn or destroy" the enemy, and that's generally the order these things would go in.

What happened, broadly speaking, in the 18th century was a rethinking of naval tactics to move away from the line-of-battle formations that had led to indecisive results and a move toward tactics that would allow one fleet to overwhelm another. I wrote about this at some length here; to quote from that answer:

Nelson had studied these tactics, and saw the potential for their decisive use. In the battle of Cape St. Vincent (1797), when Nelson was still a captain, he broke his ship out of the line of battle without orders so he could engage the Spanish van (front part of their fleet), engaging three Spanish ships with his one and taking two of them as prizes. (The exact number of ships that came to his aid is in dispute, but his 74-gun HMS Captain engaged ships of 130, 112 and 80 guns for a period of time.) Nelson could have been censured for breaking the line without orders, and could quite possibly have lost his ship in the process. The British admiral, Sir John Jervis (later created Earl St. Vincent) did not reprimand Nelson, but also did not mention his action in dispatches. (Nelson himself used his tactics for propaganda purposes, but I'm getting away from the point.)

Nelson also used the tactic of concentrating the strength of his fleet upon a smaller portion of the enemy's line in his tactics at the Battle of the Nile (sometimes called the Battle of Aboukir Bay) in 1798. That battle came after a long and frustrating summer of chasing the French from one end of the Mediterranean to another, which provided Nelson (now an admiral) with the time necessary to meet with his captains and make his tactical intentions known. When Nelson finally caught up with the French fleet, it was at anchor, but he proceeded to attack immediately with the intention of pitting his ships 2-1 or 3-1 against the front of the French line. On his own initiative, Thomas Foley, captain of HMS Goliath, noticed that there was room between the French ships and the shoal water to the west, and passed down the west side of the French line. Other ships followed, so the French line was essentially doubled, allowing the British to anchor, beat ships into submission, weigh anchor and proceed down the line.

and

As the British ships approached, Collingwood's Royal Sovereign, leading the southern column, surged ahead and was the first to engage the enemy, passing just astern of the Spanish admiral's ship Santa Ana. Victory, leading the northern column, was under fire for about 40 minutes from four ships without being able to respond, and the Franco-Spanish guns killed a number of the British crew and shot away the ship's wheel. Nelson broke the allied line at 12:45, passing astern of Villeneuve's Bucentaure and engaging the French Redoutable; Victory won that battle eventually, killing or wounding all but 99 of the approximately 650-man crew on Redoutable but Nelson himself suffered a mortal wound from a French musket ball.

The rest of the battle followed essentially as planned, with the British ships passing through the allied line and engaging multiple French and Spanish ships, combining fire whenever possible. The allied van watched the battle unfold, made a small effort to engage, fired a few guns and eventually sailed off. The British captured 22 allied ships, with the loss of none of theirs, but most of their captures were lost in a great storm the night of the battle.

So that will hopefully answer part of your question -- despite not sinking any enemy ships at Trafalgar, the British fleet beat 22 Franco-Spanish ships into submission and caused about 16,000 allied casualties, while only losing about 1,600 of their own men. There was no debate over who won that battle.

Not to shamelessly self promote, but if you're interested in naval warfare feel free to poke around in my profile.