The drying of a solvent-cast polymer film is monitored in a non-invasive way, by measuring the changes in time of dielectric properties, using interdigitated or comb electrodes. Experimentally, the vitrification of the polymer solution is observed at a distinct time, followed by the slow evaporation of solvent from the glassy state. As the solvent diffusion coefficient is a strong function of the concentration in the polymer film, removal of residual solvent proceeds at a self-decreasing rate. With a simple model, solvent mass transfer coefficients in the glassy state are determined from the experiments. It is shown that volume relaxation may be slow compared to the drying process, when preparing thin solvent-cast membranes and using solvents that diffuse relatively fast through the glassy polymer film.