Vagn Schmidt won his first major international medal for Denmark at the 1957 European Championships, when he captured silver in the K-2 1000 with Villy Christiansen, behind Fritz Briel and the non-Olympian Heinz Ackers of Germany. The following year he won bronze in the K-1 10,000 at the 1958 World Championships, behind Thorvald Strömberg of Finland and Ladislav Čepčianský of Czechoslovakia. In 1960, he partnered with his older brother Kaj in the K-2 1000 event at the Rome Olympics and placed fifth. He retired from active competition shortly after the Games, having won several national titles. Both brothers were members of the Kajakklubben Sønderstrand.