Napoleon surrendered to the British after Waterloo from Rochefort, the French Atlantic port where he sought a way to escape to North America. He formally surrendered to Captain Frederick Maitland aboard HMS Bellerophon on 15 July 1815.
After his defeat at Waterloo on 18 June and his second abdication, Napoleon left Paris and travelled west toward Rochefort. British warships were blockading the area, preventing him from sailing on one of the French vessels waiting near the Île d’Aix. With Prussian forces also pursuing him, escape became increasingly unlikely.
Napoleon chose to place himself under British protection, hoping Britain might allow him to live in England or travel to the United States. Instead, the British government treated him as a prisoner of war and sent him into permanent exile on Saint Helena.
The surrender technically occurred aboard Bellerophon off the Rochefort area rather than inside the harbour itself. That distinction explains why accounts sometimes mention the Île d’Aix or the Bay of Biscay, but Rochefort is the standard and canonical answer to this quiz question.