The US Navy did it several times during the War of 1812.
This is somewhat analogous to German naval actions in the First World War: both nations' ships were bigger, better, and more dangerous than the Royal Navy's ships, but there were far fewer of them and there were far more precious to the Germans/Americans. It's like Jutland. Almost every time British ships encountered the American heavy frigates, they would lose. But if they teamed up, they would eventually capture them, despite heavy losses (which they could afford). Remember, there were only three heavy frigates, and they were like no other ships in the world--at least, certainly unlike any French ships at the time.