Robertson learned to play golf at Dunaverty Golf Club in
Argyll, Scotland. She won the British Ladies Amateur title in 1981 at Conwy Golf Club in Caernarvonshire, Wales, having been runner-up three times: 1959 at
Royal Ascot Golf Club, 1965 at
St Andrews, and at Gullane Golf Club in 1970. She won the
Scottish Women's Amateur Championship on seven occasions. Robertson represented Great Britain and Ireland as a player on seven occasions in the Curtis Cup (1960, 1966, 1968, 1970, 1972, 1982, 1986). She was a non-playing captain in 1974 and 1976. On her ninth appearance in the competition, she experienced victory for the first time, beating the U.S. team 13–5 at the
Prairie Dunes Country Club,
Kansas in 1986. ==Notable wins==