1. The Attack on the USS Oneida; On July 19th the Royal George, Moira and Regent (sloop) attacked the only American warship on Lake Ontario at Sacket's Harbour. The British did not succeed and the Americans took all of the guns from the shore side of the Oneida and mounted them on shore as the British approached. The lack of experience and leadership of the British Provincial Marine showed and they were unable to take the Oneida.
2. The Battle of Lake Erie / Put in Bay; The British were seriously outgunned and undermanned in this one but still have a slight chance (maybe). As a "What If?" the British can set up on a more advantageous position. Perhaps on springs near a shore line.
Another "What If?"; The British could attack the Lake Erie fleet before it was refitted just after launch
3. The Attempted Capture of the Royal George on Nobember 6th 1812. Isaac Chauncey had only been in charge of the American naval forces for a few weeks but had already converted a number of merchant vessels and started building new ships. The newly formed Ontario fleet attacked the Royal George right in Kingston Harbour.
4. The so called "Burlington Races"; One of a couple of limited engagements where the two fleets fought on Lake Ontario. On September 28th 1813 the two fleets became heavily engaged briefly. Just before this they had a long range running battle of the Geonesse.
5. "What If?" May 8th 1814; Assault on Sackett's Harbour
With the launch of the Prince Regent and Princess Charlotte the British had naval dominance in the spring of 1814. They were aware that the Americans had just built the Superior but the almost complete USS Mohawk, that would turn the tables again. Drummond and Yeo wanted to do this land and sea assault but Prevost said no. Instead of this assault the British successfully took Oswego. From May to June 5th Yeo blockaded Sackett's Harbour. He then stayed at Kingston awaiting the launch of the St. Lawrence.
6. "What If?" July and August 1814; The Battle at the Mouth of the Niagara River
In July and August the Americans trapped the Star 14, Charwell 13, Netley 9, and Vincent (the Magnet 11, was blown up to avoid capture) up the Niagara with the Jefferson 20, Sylph 18, and Oneida 14. The battle would be the British ships engaging the Americans. The British controlled the forts on both sides of the river. They are outgunned but perhaps with the forts this could be a good battle.
7. "What If?" July / August 1814; The Battle of Kingston Harbour
Chauncey blockaded the British with the Superior 58, Mohawk 42, Pike 26, and Madison 23. The Jones 21, was sent to try and raid their supply line. The British had the Prince Regent 58, Princess Charlotte 40, Montreal 21, Niagara 21 and an unknown number of gunboats. Chauncy hoped for a battle but Yeo was awaiting the completion of the St.Lawrence. This could have been a decisive battle. The American ships had more long guns and larger ships. With 10 gunboats or so perhaps the British could have tried their odds.
8. Plattsburgh / Lake Champlain; with a simultaneous land battle.
9. Lake Ontario What If? 1815; The British with three first rate ships and two frigates vs two American first rate ships and their two frigates (all of the American ships were bigger than the British ships)