The solid state 59Co nmr spectra of a number of octahedral complexes are reported. In the case of sodium hexanitrocobaltate(III) the spectra have been obtained at several different field strengths and the results are analysed to give a quadrupole coupling constant of 9.4 MHz, an asymmetry parameter of zero and an axial chemical shift tensor with an anisotropy of 180 ppm. Several other complexes have been examined at high field (11.8 T) to minimize the effects of quadrupole coupling and maximize the influence of chemical shift anisotropy. The results are, where possible, compared with single crystal X-ray and low field nmr data. It is concluded that high fields are necessary to obtain reliable chemical shift anisotropy values. The conditions necessary for obtaining reasonable quality spectra from polycrystalline samples containing quadrupolar nuclei are discussed.