We show how Monte Carlo simulations with the explicit interchange of cations, the semigrand-canonical ensemble and configurational bias techniques, can be used to calculate phase diagrams for oxides, including both solid and liquid phases. We illustrate our approach with the system CaO/MgO where our techniques take full account of local structural distortion and clustering due to the large mismatch between the sizes of the two cations. All the characteristic features of the MgO/CaO phase diagram, including the eutectic point and the regions of Liquid-solid coexistence, are reproduced.