We present ab initio calculations of the electronic structure of Sr2FeMoO6 double perovskites. By considering Fe and Mo antisite defects and oxygen vacancies in various supercells, we investigate their half-metallic character, their magnetic ordering and the hyperfine fields on the Fe and Mo sites. The calculations show that the half-metallic character is lost for all considered antisite defects whereas an oxygen vacancy preserves this character. We exhibit the nearly linear relation between the number of X–O–Y bonds (X,Y=Fe,Mo) and the values of the local magnetic moment and of the hyperfine field on a given atom. The results also suggest that oxygen vacancies can be at the origin of a significant magnetization reduction.