In 1714, Wessel was court-martialled after an indecisive sea battle with a Swedish frigate. The account of the incident is verified by the legal proceedings from November 1714. On 26 July 1714, he encountered a frigate under English flag near Lindesnes, while flying a Dutch flag on the Løvendals Gallej himself. The other frigate was De Olbing Galley carrying 28 guns, which had been equipped in England for the Swedes and was on its way to Gothenburg under the command of an English captain named Bactmann. De Olbing Galley signalled for Løvendals Gallej to come closer, and as Wessel raised the Danish flag, Bactmann fired a broadside at him. In the English captain, Wessel met a tough match. The combat lasted all day, and when De Olbing Galley tried to escape in the evening, Wessel set more sails and continued the duel. The fight was interrupted by nightfall, and renewed again indecisively the following morning. Both ships were badly damaged after around 14 hours of fighting, when Wessel was running out of ammunition. He then sent an envoy to the English ship, cordially thanking the English for a good duel, and asked if he could borrow some of their ammunition in order to continue the fight. His request was denied, and the captains drank to each other's health, before the ships dispersed.
When he heard about the incident, king Frederick IV of Denmark asked for the admiralty to court-martial Wessel. He stood trial in November 1714, accused of disclosing vital military information about his lack of ammunition to the enemy, as well as endangering the ship of king Frederick IV by fighting a superior enemy force. The spirit with which he defended himself and the contempt he poured on his less courageous comrades took the fancy of Frederick IV. He successfully argued a section of the Danish naval code which mandated attacking fleeing enemy ships no matter the size, and was acquitted on 15 December 1714. He then went to the king asking for a promotion, and was raised to the rank of Captain on 28 December 1714.