When trampolining made its Olympic debut at the 2000 Olympic Games in Sydney, Cockburn was one of the twelve women to take part. Not considered a medal favourite, she performed well and earned an unexpected bronze medal.
Moving up in the world rankings, she won the 2003 world championships and established herself as the woman to beat at the 2004 Olympic Games. She placed only fifth in the qualifying round. In the final she attempted a routine with a higher degree of difficulty than any of other competitors and won the silver medal behind Anna Dogonadze of Germany.
The Canadian multiple champion continued her Olympic adventure at the Olympic Games in Beijing in 2008. As in the two previous editions, Karen was not in the first three places after the qualification rounds, and was therefore not on the provisional podium. She surpassed herself again in the final, winning her third Olympic medal - a silver. On the podium, she was accompanied by the Olympic champion, China’s Wenna He, and Uzbekistan’s Ekaterina Khilko.