Using a perturbation expansion based on a strong cubic-field zeroth-order approximation, we have obtained analytical expressions for the $g$ values of the ${{t}_{2}}^{3}$, $^{4}A_{2}$, and $^{2}F$ terms for ${d}^{3}$ impurity ions in trigonal crystal fields. We have compared these expressions whth the results of a numerical calculation in which the magnetic dipole operator was transformed to the basis of eigenvectors of the zero-field Hamiltonian computed within the complete ${d}^{3}$ configuration, and we find them to be a very good approximation. This is not true of the published $g$-value expressions which are currently available. Absolute magnetic dipole absorption cross sections and nonlinear $g$ values are also calculated. This the first time such a detailed calculation of these quantities has been made for transition-ion impurity systems. For levels derived from cubic terms other than ${{t}_{2}}^{3}$, $^{4}A_{2}$, and $^{2}E$, the analytical-perturbation techniques are not satisfactory and numerical methods must be used. We present an analysis of the $g$ values of the nominally ${{t}_{2}}^{3}$ terms, $^{4}A_{2}$, $^{2}E$, $^{2}T_{1}$, and $^{2}T_{2}$, for emerald, ruby, Zn${\mathrm{Al}}_{2}$${\mathrm{O}}_{4}$: ${\mathrm{Cr}}^{3+}$, MgO: ${\mathrm{Cr}}^{3+}$, and ZnO: ${\mathrm{Co}}^{2+}$, and of magnetic dipole absorption cross sections for centrosymmetric Zn${\mathrm{Al}}_{2}$${\mathrm{O}}_{4}$: ${\mathrm{Cr}}^{3+}$ and MgO: ${\mathrm{Cr}}^{3+}$. These systems were chosen because there are quite extensive experimental data available on them. The model parameters were determined from the zero-field energy levels, and very good agreement with experiment was obtained in our calculation of the $g$ values and absorption strengths. This provides confidence in the validity of the crystal-field model to predict the magnetic properties of at least the ${{t}_{2}}^{3}$ levels, which couple weakly to phonons.