Catherine and Robert Walpole had six children.
Robert Walpole, 2nd Earl of Orford (1701-31 March 1751), who married Margaret Rolle (17 January 1709 – 13 January 1781), later the 15th Baroness Clinton, on 26 March 1724 and had one son.
Katherine Walpole, (13 May 1703 – 22 October 1722), who died unmarried at Bath, Somerset.
Horatio Walpole (1704-24 July 1704)
Mary Walpole (c. 1706-2 January 1732), who married the 3rd Earl of Cholmondeley on 14 September 1723 and had two sons.
Horace Walpole, 4th Earl of Orford (1717–1797)
Sir Edward Walpole (born bef. 1720, death date unknown); he had an illegitimate daughter, Maria Walpole, who later married into the British Royal Family, becoming the wife of Prince William Henry, Duke of Gloucester and Edinburgh, King George III's brother.