 In 1946, Swanzy married Tirzah Garwood, widow of Eric Ravilious.After she died from cancer, in 1952 he married Henriette Van Eeghan, with whom he had two sons and a daughter.In his honour, the Henry Swanzy Award for Distinguished Service to Caribbean Letters was announced by the NGC Bocas Lit Fest in 2013, as an "annual lifetime achievement award to recognise service to Caribbean literature by editors, publishers, critics, broadcasters, and others".