Element- and orbital-selective x-ray absorption and magnetic circular dichroism measurements are carried out to probe the electronic structure and magnetism of Ir 5d electronic states in double perovskite Sr2MIrO6 (M=Mg, Ca, Sc, Ti, Ni, Fe, Zn, In) and La2NiIrO6 compounds. All the studied systems present a significant influence of spin-orbit interactions in the electronic ground state. In addition, we find that the Ir 5d local magnetic moment shows different character depending on the oxidation state despite the net magnetization being similar for all the compounds. Ir carries an orbital contribution comparable to the spin contribution for Ir4+ (5d5) and Ir5+ (5d4) oxides, whereas the orbital contribution is quenched for Ir6+ (5d3) samples. Incorporation of a magnetic 3d atom allows getting insight into the magnetic coupling between 5d and 3d transition metals. Together with previous susceptibility and neutron diffraction measurements, the results indicate that Ir carries a significant local magnetic moment even in samples without a 3d metal. The size of the (small) net magnetization of these compounds is a result of predominant antiferromagnetic interactions between local moments coupled with structural details of each perovskite structure.