Stjerne has participated in five World Junior Championships. He played as third for Kenneth Jørgensen in 2004 and 2005, finishing outside of the playoffs in both years. He then skipped his own team at the World Juniors in 2006, 2007, and 2008, finishing 5th, 4th, and 7th, respectively. Then, in the 2009 World Junior Curling Championships, Stjerne and his team made the playoffs as the second-ranked team. They were defeated by Canada in the page 1 vs. 2 game, but rebounded with a win over the United States in the semifinal and defeated Canada in the final to win the gold medal.
Stjerne skipped a team at the 2010 European Curling Championships, and led his team to the playoffs. Stjerne returned the next year at the 2011 European Curling Championships and again made the playoffs, earning the bronze medal.
Stjerne represented Denmark at the 2012 World Men’s Curling Championship in Basel, where Denmark finished outside of the playoffs. Later that year, he led Denmark to a 4th place finish at the 2012 European Curling Championships. He followed this up by placing 4th at the 2013 Ford World Men’s Curling Championship, and again finishing 4th at the 2013 European Curling Championships. Stjerne skipped Denmark at the 2014 Winter Olympics, leading the team to a 6th place finish with a 4-5 record.
In his return to Basel to represent Denmark at the 2016 World Men’s Curling Championship, Stjerne led his rink to a silver medal, Denmark’s best world championship result ever.