We have investigated the magnetic moment of the W ion in the ferrimagnetic double perovskites Sr2CrWO6 and Ca2CrWO6 by x-ray magnetic circular dichroism at the W L2,3 edges. In both compounds a finite negative spin and positive orbital magnetic moment was detected. The experimental results are in good agreement with band-structure calculations for (SrCa)2CrWO6 using the full-potential linear muffin-tin orbital method. It is remarkable that the magnetic ordering temperature, TC, is correlated with the magnetic moment at the "nonmagnetic" W atom. © 2005 The American Physical Society.