Ragnheiður made her Olympic debut, as Iceland's youngest swimmer (aged 19), at the 2004 Summer Olympics in Athens. She qualified for two swimming events by attaining B-standard entry times of 26.34 (50 m freestyle) and 56.74 (100 m freestyle). In the 100 m freestyle, Ragnheiður finished last in heat three and fortieth overall with a time of 58.47 seconds. In the 50 m freestyle, Ragnheiður almost snared out of triumph in heat five by a hundredth of a second (0.01) behind Luxembourg's Lara Heinz, finishing second and thirty-first overall in 26.36 seconds.