We present studies of orbital magnetic moments of CrO2 and Fe3O4 by measuring magnetic circular dichroism (MCD) in soft X-ray absorption. The results show that Fe3O4 exhibits large orbital moments, as a consequence of the strong Coulomb interactions of Fe 3d electrons. In contrast, orbital moments of Cr in CrO2 are nearly quenched, revealing that Cr 3d electrons are strongly hybridized with O 2p electrons and more delocalized as compared with those of Fe in Fe3O4. Comparing the MCD data with the band structure calculations based on local spin density approximation with on-site Coulomb energy U taken into account, we conclude that to include the on-site Coulomb interactions of 3d electrons is essential for adequately describing the electronic structure of CrO2 and Fe3O4.