Impedance spectroscopy was applied to Portland cement and its carbon nanotubes (CNT) composites to measure and describe the electrical conductance phenomena and their dependency on the moisture. Two series of composites were prepared, one with multi-walled, and the other with single-walled CNTs. The percolation concentration was reached only with the single-walled CNTs between 0.10 and 0.25 wt%; it was therefore possible to compare a percolative and a non-percolative system. The kinetic of the drying process was measured in the range of 24 h and described by a decay model with a stretched exponential to be correlated with the composite composition. The polarization phenomena occurring in the materials before and after the moisture removal were modelled with logistic sigmoid and explained by the morphology. In particular, the three found sigmoid were correlated to the polarization phenomena occurring at well-defined structural levels of the specimens. Their mathematical definition was shown to be fundamental for a correct interpretation of the Cole-plots of the real conductivity. Such phenomena presented a peak of intensity at a well define frequency but their effects spread across a broad range of Hertz. Moreover, over the AC frequency of 10 Hz, the conductive effect of the moisture overlapped the conductivity increase caused by the percolative network of the CNT. A dry sample is therefore necessary for accurately evaluating the source of the conductivity, a distinction which is crucially important for sensing applications.