Her first World Championships participation came in 1991. Here, she finished seventh in the 400 m hurdles. At her first Olympic Games in 1992 she only reached the semi-final of the 400 m hurdles competition, but finished sixth in the 4 x 400 m relay with teammates Uta Rohländer, Linda Kisabaka and Anja Rücker. At the 1993 World Championships Meißner finished third in her semi-final heat, but this was not enough to reach the final round. Instead she competed once more on the 4 x 400 m relay team, finishing fifth with Sandra Seuser, Anja Rucker and Linda Kisabaka. The same year, however, Meißner competed at the 1993 Summer Universiade and won a gold medal in the 400 m hurdles. She beat Debbie-Ann Parris of Jamaica with a margin of only 0.01 seconds.