We discuss the effects of the spin-orbit interaction on heavy-atom organic magnets with specific reference to a series of isostructural sulfur- and selenium-based radical ferromagnets of tetragonal space group P4̅ 21m. By using a perturbative approach, we show the spin-orbit effects lead to a pairwise anisotropic exchange interaction between neighboring radicals that provides an easy magnetic axis running parallel to the c-axis. Estimates of the magnitude of this magnetic anisotropy explain the significant increase in the coercive fields by virtue of selenium incorporation. Complementing this theoretical discussion are the results of ferromagnetic resonance studies, which provide an experimental verification of both the magnitude and symmetry of the spin-orbit terms. Taken as a whole, the results underscore the importance of heavy atoms and crystal symmetry in the design of molecular ferromagnets with large magnetic anisotropy and high ordering temperatures.