Solubilities of additive molecules whose molecular sizes exceed the typical dimensions of free volume cavities pre-existing in amorphous polymer melts and glasses I cannot readily be computed in molecular simulations. In this paper, we perform molecular dynamics simulations of a soft-cavity reference state ensemble, which contains a soft-core, fast diffusing, Lennard-Jones particle in a rigid-chain polymer matrix. By means of the Zwanzig thermodynamic perturbation formalism, the soft particle has been perturbed to various real-solute end-states. It is shown that with this approach it is possible to overcome some of the free energy sampling problems related to. the insertion of large solutes and slow diffusion in the end-state. We have calculated the excess chemical potentials of propane, chloroform, and dimethyl sulfoxide in liquid bisphenol A-polycarbonate and show that a single simulation of the reference state is sufficient to obtain statistical accuracies within error bars of 0.5-0.8 k(B)T The method is particularly useful for calculating solubility ratios of large molecular solutes with approximately equal excluded volume radii.