Cranstoun reached the rank of Lieutenant on 19 October 1776 and Captain on 31 January 1780.
He commanded HMS Belliqueux at the Battle of St. Kitts in January 1782 and after the Battle of the Saintes in April was sent home with the despatches (in which he was mentioned) bearing news of the victory.
Lord Cranstoun was married on 19 August 1792 to Elizabeth, youngest daughter of Lieutenant-Colonel Lewis Charles Montolieu and sister-in-law of Alexander Murray, 8th Lord Elibank and of James Bland Burges (later Sir James Bland Lamb, 1st Baronet).
[2] They had no children, so the title passed to Lord Cranstoun's nephew.
Lady Cranstoun died on 27 August 1797, aged twenty-seven.