At the 1964 Winter Olympics in Innsbruck, Saubert won a bronze medal in the slalom and a silver medal in the giant slalom, losing only to French sisters Christine and Marielle Goitschel. Saubert was the only multiple medal winner for the U.S. in those Olympics, and her medals represented two of the six medals won by the entire United States team. Two years later, Saubert finished fourth in the slalom at the 1966 World Championships in Portillo, Chile. Following the world championships, held in August, Saubert retired from international competition at age 24.