A free energy formulation of localised canting in substituted magnetic oxides is described. In contrast with earlier attempts at mathematical formulations of localised canting, quantities which may be replaced by average values and those which must be considered on a site-to-site statistical basis are clearly delineated. In addition, the use of local canting to determine average split-sublattice molecular-field directions is done in an iterative self-consistent manner. The theoretical curves of magnetisation versus level of non-magnetic substituent are somewhat rounded, compared with the linear dependences which result from the Yafet-Kittel model. For a given ratio of exchange parameters, canting commences at somewhat lower substituent levels than from the Yafet-Kittel model. Comparisons with experimental magnetisation data for YIG with Ge, Si, Zr, and Sc substitutions and for Li-Zn ferrite indicate several things: (a) no single exchange parameter can provide a good theoretical fit to the data for a given system over the full range of substitution; (b) the theoretical curves, when fitted to the data, indicate a decrease in the inter- to intrasublattice exchange integral ratio for large substitutions where canting effects become pronounced; (c) the fits, when based on the assumption of a randomly split sublattice and equal intra- and intersublattice interactions for the two parts of the split sublattice, are consistent with reported exchange constant ratios for the unsubstituted oxides.