Meineke was strongest in the early 1980s, winning a gold medal as part of the East German team for the 4 × 100 m freestyle relay in the 1981 European Aquatics Championships, as well as two silver medals in the same year for the 200 meter and 100 meter freestyle. In the same year, she also established a world record in the short course 100 m freestyle, with a time of 54.04 seconds. While her performance at the 1982 World Aquatics Championships was similarly strong, the pinnacle of her career was a sweep of five golds at the 1983 European Aquatics Championships in Rome.