Since her debut in international competitive sport, Norberg has become European champion seven times (1988, 2001, 2002, 2003, 2004, 2005, 2007). Her greatest successes to date have been winning the gold medal at the 2005 World Cup in Paisley , the 2006 World Cup in Grande Prairie and winning the 2006 Winter Olympics in Turin (as a skip in a team with Eva Lund (third), Cathrine Lindahl (second), Anna Svärd (lead) and Ulrika Bergman (replacement)). Norberg has also participated in six other world championships. In 1988, 1989, 1991 and 2003 she won the bronze medal, respectively, and the silver medal in 2001 and 2009. In 2010 she won gold at the Winter Olympics for the second time with the same team in Vancouver . In the final they beat the Canadians to Skip Cheryl Bernard 7: 6 after a stolen stone in the additional end.
After the Olympic Games, the team separated and Norberg was skip the team around Cecilia Östlund .