Stenderup began playing football in the youth teams of Vanløse in 1996, before joining Brøndby's academy as a 15-year-old, after a one-year stint at B.93.
[2][3] On 24 August 2008, he made his professional debut for Brøndby in a 7–1 Danish Cup win over lowly Frem Sakskøbing, replacing Mikkel Bischoff in the 73rd minute.
[5] However, he had to wait until 3 October 2010 for his league debut, as head coach Henrik Jensen started him in a 1–0 home loss to AC Horsens.
[6] In the game, he put up a good performance, albeit making a crucial mistake which led to Gilberto Macena's lone goal which proved decisive.
[8] On 28 July 2011, Stenderup made his European debut, starting in Brøndby's 2–0 away defeat against Austrian club SV Ried in the third-qualifying round of the UEFA Europa League.