The osmotic molecular dynamics method (OMD) is used to calculate activity coefficients for vapour-liquid equilibria (VLE) and liquid-liquid equilibria (LLE) predictions. The previously reported OMD methodology is refined and applied to mixtures of polar, structured molecular fluids. Other computer simulation approaches to phase equilibria prediction are discussed briefly, and comparison to recent Gibbs Ensemble Monte Carlo (GEMC) results is made. OMD-predicted activity coefficients are compared to experimentally-measured activity coefficients for six industrially-significant binary mixtures (methanol/n-hexane, n-hexane/n-pentane, chloroform/acetone, chloroform/methanol, methanol/water, chloroform/n-hexane). Molecular model inadequacies, especially cross-parameters between unlike molecules, are shown. A single cross-parameter for the acetone/chloroform binary is modified to produce good agreement with experimentally-measured activity coefficients. Also, OMD-derived LLE predictions are produced for the methanol/n-hexane system and compared with experimentally-measured LLE data.