Ptychographic X-ray computed tomography (PXCT) allows for a non-destructive, three-dimensional mapping of the electron density. Its quantitativeness combined with a resolution in the 100 nm range makes it a suitable tool for the assessment of densities of the individual phases in complex materials, such as hardened cement pastes. Here we present results of an experiment performed on a cylindrical sample of epoxy-impregnated hardened cement paste of about 30 μm in diameter. Two-dimensional cross sections of the three-dimensional electron density map show a microstructure that bears distinct similarity to that observed by back-scattered scanning electron microscopy. Domains of various residues of cement grains, calcium hydroxide, calcium carbonate, epoxy-resin impregnated calcium silicate hydrates, epoxy-resin impregnated porosity, and unimpregnated porosity are revealed and are manifested as distinguishable peaks in the histogram of the three-dimensional electron density map. On assumptions of (i) a priori knowledge of the chemical composition and (ii) the purity of the analysed regions, the mass densities of the above mentioned individual material phases are estimated. The potential of PXCT for the science of cement and concrete is discussed.