Sebestyén competed at the 2002 Winter Olympics and placed 8th; she was also 8th at that season's Worlds. The next season, she earned her first European Championships medal, a bronze. In 2004, she won the 2004 European Figure Skating Championships, becoming the first Hungarian woman to win that competition. She later finished 6th at the 2004 Worlds, which would prove to be her best result in that event.