Precipitation hardening is a key strategy for improving the overall strength and ductility 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 models have been proposed to quantify the influence of precipitate shape, size, and volume fraction on the CRSS, there is considerable scatter in the predictions. Moreover, the role of the local stress state at the precipitate-matrix and precipitate-twin interface on hardening remains to be understood. In this study, we systematically investigate the interactions between {101 ̅2} twins in Mg and Mg-Al precipitates to scrutinize the predictive capabilities of proposed hardening models, using atomistically-informed 3D phase field simulations. Ultimately, the hardening data is used to propose a model for the CRSS required for continued twinning deformation in the presence of precipitates.