The program {\sc Duo} (Yurchenko {\it et al.}, Computer Phys. Comms., 202 (2016) 262) provides direct solutions of the nuclear motion Schr̈odinger equation for the (coupled) potential energy curves of open shell diatomic molecules. Wavefunctions from {\sc Duo} are used to compute Landé $g$-factors valid for weak magnetic fields, the results are compared with the idealized predictions of both Hund's case (a) and Hund's case (b) coupling schemes. Test calculations are performed for AlO, NO, CrH and C$_2$. The computed $g_J$'s both provide a sensitive test of the underlying spectroscopic model used to represent the system and an indication of whether states of the molecule are well-represented by the either of the Hund's cases considered. The computation of Landé $g$-factors is implemented as a standard option in the latest release of {\sc Duo}. ; Comment: This is a revised version which includes the correct Figure 5 (compared to the published version)