Four schemes are presented that can lead to third-harmonic generation in crystals containing colour centres. In addition to calculating the corresponding third-order susceptibilities, we discuss the means of satisfying the phase matching condition for each scheme. We find that the anomalous dispersion near a resonance, in both linear and nonlinear response regimes, can be used to advantage in the phase-matching condition and also in enhancing the value of χ(3)(3ω). Our results suggest that by employing a suitable host plus electronic impurity combination it would be possible to have a reasonable value for χ(3)(3ω = ωPLUωPLUω) and good conversion efficiency of third-harmonic generation in the solid state.