 During her time in university, Wæver worked as one of the first female continuity announcers in Danmarks Radio (DR).She is best known for presenting the Eurovision Song Contest in Copenhagen in 1964, a position for which she says she was chosen over her peers because of her willingness to do it.The contest was famously overshadowed by a political protest from a man who trespassed onto the stage holding a banner reading "Boycott Franco and Salazar".