Robert John Anderson Carnwath, Lord Carnwath of Notting Hill, Kt, CVO, PC (born 15 March 1945), is a former British Supreme Court judge. The son of Sir Andrew Carnwath KCVO, Robert Carnwath was educated at Eton College, where he won the Newcastle Scholarship, and Trinity College, Cambridge. Carnwath is the Chairman of the Advisory Council for the Institute of Advanced Legal Studies. He plays the piano and viola, as well as singing in the Bach Choir.