Ragnheiður ta fara gasar Olympics, a matsayin mafi ƙanƙanta na Iceland (shekaru 19), a Wasannin Olympics na 2004 a Athens. Ta cancanci shiga wasannin ninkaya guda biyu ta hanyar cimma daidaitattun shigarwar B na 26.34 (50 m freestyle) da 56.74 (100 m freestyle). A cikin mita 100 na 'yanci, Ragnheiður ya gama na ƙarshe a zagayen uku kuma na arba'in a gaba ɗaya tare da lokacin 58.47 seconds. A tseren mita 50 na 'yanci
, Ragnheiður kusan ya kama nasara a zagaye na biyar ta kashi dari na biyu (0.01) a bayan Lara Heinz na Luxembourg, ya gama na biyu da talatin da ɗaya a cikin dakika 26.36.