At the 1924 Paris Olympics, Osiier competed reached the finals in individual foil by winning his pool in the first 4 rounds. In the finals, he was victorious in only one bout (out of six), and finished in 6th place. He also finished in 6th place in individual sabre after winning two of seven matches in the final pool (he again won all his earlier pools). In the team events, Denmark reached the semifinals in foil before losing to Italy and Belgium, and were eliminated in the quarterfinals in épée.