Salmeen was born in Ann Arbor, Michigan. She was a competitive swimmer by the age of 9, and became a standout swimmer at Huron High School in Ann Arbor, where she was co-captain of the girls' swimming team for two years. While at Huron, Salmeen was three-time state champion in the 500-yard freestyle, and once in the 100-yard butterfly. Salmeen went on to swim at the University of California, Los Angeles (UCLA), where she was a co-captain, four-time All-American, and an NCAA national champion in the 200-yard butterfly. She won a bronze medal in the 200-meter butterfly at the 1995 World University Games in Fukuoka, Japan. Salmeen qualified for the U.S. Olympic Team for the 1996 Summer Olympics in Atlanta, Georgia, where she earned a gold medal for swimming for the winning U.S. team in the preliminary heats of the women's 4×200-meter freestyle relay. In individual competition at the Olympics, she finished 4th in the B Final (12th overall) in the women's 200-meter butterfly.