Wilmot was the second son of Robert Wilmot (1669–1738), of Osmaston Hall, near Derby, and his wife Ursula, who was the daughter of Sir Samuel Marow, Bt, of Berkswell, Warwickshire.
John Eardley Wilmot PC (1709–1792), Chief Justice of the Common Pleas 1766–1771
In 1768, he married Maria Wilmot, the daughter of Sir John Eardley Wilmot, Chief Justice of the Common Pleas.
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Robert Wilmot was the elder son of Robert Wilmot (died 1738) of Osmaston Hall, and his younger brother was the judge John Eardley Wilmot (1709-1792).