[1] After being injured in the Battle of the Somme during the First World War, Stedman was selected to carry the flag for Australasia at the Opening Ceremony of the 1920 Summer Olympics (Australia and New Zealand sent a combined team).

In an all-Australian team, Stedman combined with Henry Hay, William Herald and Frank Beaurepaire to claim silver in the 4×200-metre freestyle relay.

The American team, led by Duke Kahanamoku, won by an extremely large margin of 21 seconds.

Stedman also competed at the 1924 Summer Olympics in Paris, with less success, where he was eliminated in the semifinal of the 100-metre freestyle and the heats of the 200-metre breaststroke.

Stedman was a regular competitor in the Race to Prince's Bridge, the annual three-mile Yarra River swim.