For the most part reorganization and an uneasy recovery. You have to keep in mind that this was a really messy era for Scandinavia. In 1800 both Sweden (who owned Finland) and Denmark (who owned Norway) were members of the league of armed neutrality. In 1801 Britain basically said "fuck this" and attacked Denmark, wrecking the navy, occupying their colonial holdings and forcing them to leave the coalition (and effectively recognizing British naval superiority in the region).

Denmark responded to this by declaring themselves even neutraler than the league of armed neutrality (which was in effect pro Russian and anti-British). However, since Napoleon was the real power in the area Denmark came under a lot of presure to put their navy at Napoleon's disposal. By 1807 Britain said "Well we can't have that" and attacked Denmark again, making what was left of the navy surrender and basically forcing Denmark into an alliance with Napoleon.

Napoleon forces Denmark to declare war on Sweden in 1808 but since the British are holding the sound between Denmark proper and Sweden and Denmark has no navy they're pretty limited in what they can do. Sweden, having decided that Britain is looking like a good bet, sides with them.

Since Sweden can't and won't honour previous pledges to close the Baltic to foreign warships (effectively meaning British in this case) the Anglo-Russian war leads to Russia declaring war on Sweden. The king of Sweden had wildly unrealistic expectations on the army's ability to hold off Russia and seriously underestimated Russia's ability to attack Finland in the winter. As a result Sweden lost all of Finland to Russia (although given the vast numerical inferiority, supply shortages and often disastrous plans the Swedish army did remarkably well, by which I mean it took the better part of two years for Russia to win).

Meanwhile the war between Sweden and Denmark prompted Sweden to try an invasion of the only part of Denmark we could effectively reach (with the navy occupied against Russia), Norway. With the lions share of the army busy losing to Russia in Finland the Swedish invasion of Norway fared poorly. Really poorly, and Sweden withdrew.

Meanwhile in Norway the mountain monkies... eh... Norwegians, cut off from Denmark, are discovering that ruling themselves might not be so bad. They've even beaten back the Scandinavian bully in the east. Nationalism is on the rise.

Meanwhile Sweden, somewhat dismayed by recent territorial setbacks, decided that "king by the grace of god" might be more like "king by general tolerance of his subjects" and promptly dethrones Gustav IV and elects Charles XIII as King. He, however, is old, frail and childless so Sweden looks around for a King, finding Christian August of Augustenborg, the Danish commander who had lead the defense of Norway against Sweden. Charles XIII formally adopts him and he procedes to greet the news by promptly dying at age 41.

Again lacking a suitable heir to the throne Sweden turns again to our old enemies and elects Jean Baptiste Bernadotte, a french commander, as King. He is promptly presured to join the anti-Napoleonic coalition but decides he wants Norway as compensation for the loss of Finland (since demanding Finland back, whilst allied to Russia who had just taken it, was not a great idea). The great powers somewhat reluctantly agree on the condition that this happens only after Napoleon is defeated.

Bernadotte basically says "okay" and joins the Napoleonic war, focusing primarily on Denmark. Sweden participates in the Battle of Leipzig, a very bloody affair. Following the Battle of Leipzig Bernadotte takes the Northern Army up through Denmark which prompts a Danish surrender.

In the treaty of Kiel Denmark gives up Norway to Sweden, something that the Norwegians didn't really think the Danes were allowed to do since they had, in the meantime, written their own constitution and basically taken to ruling themselves.

A lot of politics followed until 1814 when politics led to a little war that neither side was overly enthusistic about. To end matters Sweden offers a settlement to Norway, basically guaranteeing Norwegian independece in all matters except foreign policy. After several rounds of discussions, amendments and politics the Norwegians vote to accept a personal union with Sweden and elect the Swedish king as King of Norway (note, elect him, not accept his claim).

So by the time of the Concert of Europe both Sweden and Denmark, the main powers of Scandinavia, were exhausted, destabilized and weary. Since we're talking about a relatively short period of time, not a lot happened. Denmark was licking its wounds after the war. Norway and Sweden were exploring their new and somewhat uneasy alliance and Finland was quiet unhappily being a puppet of Russia.

Mostly from Union och demokrati: de förenade rikena Sverige och Norge 1814–1905