We study experimentally and theoretically the electronic and magnetic properties of two insulating double perovskites that show similar atomic and electronic structure, but different magnetic properties. In magnetization measurements, La 2 ZnIrO 6 displays weak ferromagnetic behavior below 7.5 K whereas La 2 MgIrO 6 shows antiferromagnetic behavior (AFM) below T N = 12 K. Electronic structure calculations find that the weak ferromagnetic behavior observed in La 2 ZnIrO 6 is in fact due to canted antiferromagnetism. The calculations also predict canted antiferromagnetic behavior in La 2 MgIrO 6 , but intriguingly this was not observed. Neutron diffraction * Email: gcao1@utk.edu * Email: dmandrus@utk.edu measurements confirm the essentially antiferromagnetic behavior of both systems, but lack the sensitivity to resolve the small (0.22 μ B /Ir) ferromagnetic component in La 2 ZnIrO 6 . Overall, the results presented here indicate the crucial role of spin-orbit coupling (SOC) and the on-site Coulomb repulsion on the magnetic, transport, and thermodynamic properties of both compounds. The electronic structure calculations show that both compounds, like Sr 2 IrO 4 , are J eff = 1/2 Mott insulators. Our present findings suggest that La 2 ZnIrO 6 and La 2 MgIrO 6 provide a new playground to study the interplay between SOC and on-site Coulomb repulsion in a 5d transition metal oxide.