Schmidt's first international appearance was at the 1984 World Junior Curling Championships, where he skipped the Danish team to a 9th-place finish.

Later that year, he won a silver medal at the 1997 European Championships, where he lost to Germany (skipped by Andy Kapp) in the final.

Schmidt didn't return to international competition until the 1999 Ford World Men's Curling Championship, where he placed 6th.

Later in the year, he won another silver at the Euros, losing to Scotland this time in the final, skipped by Hammy McMillan.

In 2000, he won another European silver medal, losing to Finland (skipped by Markku Uusipaavalniemi) in the final.