Computer simulation of impedance spectroscopy (IS) of hydrating cement paste, using a three-dimensional, four-phase model, is described. Two puzzling features of experimental IS results, the possible offset resistance in the Nyquist plot and the sharp decrease in normalized conductivity within the first 50 h of reaction, have been studied using the computer simulation model. Insight is provided into these features using the ability of the model to compare quantitatively microstructure and properties. It is concluded that the offset resistance is an experimental artefact, and does not directly relate to microstructure. The drop in conductivity during the first 50 h is shown to be a consequence of a gradual shift from parallel-dominated to series-dominated behaviour of the electrical conductivity, as microstructural modifications take place during hydration, causing the capillary pore structure to become more tortuous. This tortuousity can also explain the high-frequency impedance behaviour in terms of a two-are response.