Ildikő Ságiné-Ujlakiné-Rejtő has the unusual distinction of winning Olympic medals under three different names – as Miss Rejtő in 1960, as Mrs. Ujlakiné-Rejtő in 1964 and 1968, and as Mrs. Ságiné-Ujlakiné-Rejtő in 1972 and 1976. She shares this with German speed skater Andrea Ehrig-Schöne-Mitscherlich.

Ildikő won seven Olympic medals, including gold in the individual and team foil in 1964. At the World Championships, she won five titles – individual foil in 1963, and team foil in 1959, 1962, 1967, and 1973, and 15 medals in all, adding seven silvers and three bronzes. Her first international titles came in winning the World Junior title in 1956 and 1957. She continued competing as a senior, winning the World Veterans Championship in 1999. Ildikő was named Hungarian Sportsperson of the Year in 1963 and 1964. She was later inducted into the International Jewish Sports Hall of Fame. She accomplished all this despite being almost completely deaf.