On 20 March 1782 he married Lady Florinda Trench (3 August 1766 – 9 February 1851), born in
Twyford, Westmeath to
William Power Keating Trench, 1st Earl of Clancarty and
Anne Gardiner, Countess of Clancarty. William and Florinda had no children, and when Handcock was created
Baron Castlemaine, of
Moydrum (in the
Peerage of Ireland) on 21 December 1812 the title had a special
remainder "failing heirs of his body to his brother". He was further created
Viscount Castlemaine on 12 January 1822 but without a
special remainder. On his death the viscountcy became extinct. His barony passed to his brother, whose descendants still hold the title. ==Arms==