He married Barbara Villiers, daughter of the Earl of Jersey, in 1725. They had no children, although he had previously had an illegitimate daughter Elizabeth Orde. The Baronetcy became extinct upon his death. He bequeathed his estates at Allendale, Northumberland and Wallington Hall, Cambo to his nephew Sir Walter Calverley, 2nd Baronet of Calverley, conditional upon the latter's marriage to Elizabeth Orde, Blackett's natural daughter and his change of name to Blackett.