The problem of extracting effective diffusivities of cement pastes on the basis of X-ray microtomography images is considered. A general computational homogenization framework is developed and applied to a variety of cement pastes whose microstructure has been digitized to a resolution of 1 mu m. At this resolution, important submicron features are not resolved. Consequently, we propose a methodology whereby the pore space is ascribed a diffusivity less than the free diffusivity. For this purpose, a simple rule that incorporates microtomography data is proposed and shown to yield satisfactory results.