Precipitation strengthening is a key strategy for improving the overall strength of Mg alloys. In Mg-Al alloys, basal precipitates are known to impede the growth of deformation twins resulting in a substantial increase in the critical resolved shear stress (CRSS) necessary for continued growth. Although several analytical models have been proposed to quantify the influence of precipitate shape, size, and distribution on the CRSS, the accuracy/scope of these models has not been fully assessed. Here, we systematically investigate the interactions between tension twins and precipitates in Mg-Al alloys, using atomistically-informed phase-field simulations, to scrutinize the predictive capabilities of analytical strengthening models. Then, we propose modifications to these model forms to improve their predictiveness. Finally, we test the predictiveness of the extended models in extrapolating to experimental strengthening data. Ultimately, the results presented here help elucidate the fidelity of the analytical models in predicting precipitation strengthening effects in technologically important alloys.