We use molecular simulations to investigate the wetting behavior of water at flat polar surfaces. Introducing a computational procedure based on thermodynamic integration methods, we determine the equilibrium water film thickness on the surface at given vapor density as well as the corresponding change of the surface free energy. The wetting film is relevant on polar surfaces near the wetting transition and significantly alters the surface contact angle. For thin films, the surface free energy change increases linearly with the thickness, as predicted by simple thermodynamic arguments. For thick films we observe deviations from linearity, which we rationalize by the formation of hydrogen bonds between water molecules in the film. Our approach provides an efficient and accurate technique to calculate the wetting properties of surface layers, which we verify by simulating water droplets on the surfaces.