ZnGeN2 and other heterovalent ternary semiconductors have important potential applications in optoelectronics, but ordering of the cation sublattice, which can affect the band gap, lattice parameters, and phonons, is not yet well understood. Here the effects of growth and processing conditions on the ordering of the ZnGeN2 cation sublattice were investigated using x-ray diffraction and Raman spectroscopy. Polycrystalline ZnGeN2 was grown by exposing solid Ge to Zn and NH3 vapors at temperatures between 758 degrees C and 914 degrees C. Crystallites tended to be rod-shaped, with growth rates higher along the c-axis. The degree of ordering, from disordered, wurtzite-like x-ray diffraction spectra to orthorhombic, with space group Pna2(1), increased with increasing growth temperature, as evidenced by the appearance of superstructure peaks and peak splittings in the diffraction patterns. Annealing disordered, low-temperature-grown ZnGeN2 at 850 degrees C resulted in increased cation ordering. Growth of ZnGeN2 on a liquid Sn-Ge-Zn alloy at 758 degrees C showed an increase in the tendency for cation ordering at a lower growth temperature, and resulted in hexagonal platelet-shaped crystals. The trends shown here may help to guide understanding of the synthesis and characterization of other heterovalent ternary nitride semiconductors as well as ZnGeN2.