Magnetic measurements were made on α-CoMoO4 powder and β-CoMoO4 thin film samples. α-CoMoO4 powder showed antiferromagnetic ordering below 13 K and two sharp spin flop transitions with complete magnetic saturation after the second transition (>5 T). A magnetic phase diagram for α-CoMoO4 was constructed, revealing three low-temperature magnetic phases: an antiferromagnetic phase at low field, an intermediate spin-flop phase, and a paramagnetic phase at high field. Two well-defined magnetisation plateaus were observed either side of the spin-flop phase: the first occurred with a moment per Co ion of 1/3 of spin saturation (where Co moments are completely aligned to the applied magnetic field), whereas the second occurred at a moment per Co ion matching calculations for spin saturation (3 μB per Co). No geometric origin for this factor of 1/3 could be found. Hysteresis was observed around the first spin-flop transition, indicating the presence of spin canting or magnetic domains under an applied field. The first successful fabrication of CoMoO4 thin films was achieved via RF magnetron sputtering, yielding β phase films which remain in the β phase upon cooling. The β-CoMoO4 thin films demonstrated antiferromagnetic ordering below 10 K. While two spin-flop transitions are seen in the β phase films (with a hysteresis around the first), spin saturation is not reached in fields up to 6 T, suggesting the existence of a third spin reorientation at higher field. A magnetic phase diagram was also constructed for the β-CoMoO4 film, which demonstrated the same three low-temperature magnetic phases, though with lower critical fields and transition temperatures. Comparisons with isostructural Ni and Mn molybdates showed that the key differences in the α and β phases arise from the different coordination of the Mo tetramers, indicating differences in magnetic properties in both phases arise from variations in the inter-tetramer exchange coupling.