Ragnheiður akaita mutambo wake wekutanga weOlympic, semumhanyi mudiki weIceland (ane makore gumi nemapfumbamwe), kumaOlympics ezhizha ra2004 muAthens. Akakwanisa kupinda mumakwikwi maviri ekushambira nekuwana B-standard yekupinda nguva ye26.34 (50 m freestyle) uye 56.74 (100 m freestyle). Mumakwikwi emamita zana akasununguka, Ragnheiður akapedza ari wekupedzisira mumakwikwi matatu uye wechina pakupedzisira aine nguva yemasekondi 58.47. Mumakwikwi emamita 50 akasununguka
, Ragnheiður akapotsa akabata kukunda mumakwikwi mashanu nehafu yechipiri (0.01) kumashure kweLara Heinz weLuxembourg, achipedza wechipiri uye makumi matatu nemasere mumasekondi 26.36.