Ab initio calculated X-ray absorption and X-ray magnetic circular dichroism (XMCD) spectra at the Cr and Re L2, 3 edges for the double perovskite Sr2CrReO6 are compared with experiment. The main features of the experimental spectra are reproduced by the calculations, however, the amplitudes of several structures are significantly over- or underestimated. The calculated spin and orbital magnetic moments for Cr and Re agree with those obtained by means of XMCD sum rules, except for the Cr orbital moment, illustrating that numerical uncertainties can be large for small moments. It is also argued that the Re moments are induced and not intrinsic. © Europhysics Letters Association, 2009.