"Invincible" went on to form part of Francis Samuel Drake's squadron at the Invasion of Tobago in May 1781, after which time Saxton was well enough to resume command, and to sail with her to North America with Sir Samuel Hood's force. He was with Hood's squadron, as part of the larger fleet under Sir Thomas Graves, at the Battle of the Chesapeake on 5 September, though Hood's force in the rear took little part in the action. Saxton then returned to the West Indies with Hood's force and was present at the Battle of Saint Kitts on 25/26 January 1782. Again his ship was only lightly engaged, and suffered casualties of only two of her men wounded. Hood then despatched "Invincible" to Jamaica to be refitted, after which Saxton sailed in July 1782 to join Admiral Hugh Pigot off the American coast. He was off New York from September until October 1782, and in November took part in the blockade of Cape François. He was present with Edmund Affleck's squadron at Puerto Cavello in February 1783, and on 19 February "Invincible" retook the 44-gun , which two French frigates had captured shortly before.