Understanding the physical origins of the electrical response of cement-based materials is crucial to enhance the capabilities of non-destructive techniques, especially those based on resistivity or electrochemical measurements deployed in durability assessment and monitoring study of concrete structures. In this article, we show that using the information on the composition-dependent dynamics of ions obtained from molecular dynamics simulations improves the estimates of the electrical conductivity of the pore solutions. The link between ion dynamics and electrical conductivity in aqueous solutions is discussed from the fundamentals of ionic transport at the molecular scale. Also, we quantify the variability of pore solution conductivity. For validation, modeling results are extensively compared to experimental measurements on various cement systems. We show that a dilution effect explains the $w/c$-dependency of the electrical conductivity of the pore solutions. Also, accounting for the age-dependency of ionic diffusion in the pore solution is crucial to capture the age-dependency of the electrical conductivity of the pore solutions. These results are significant because they allow the prediction of the conductivity for various compositions of interest that may be encountered in cement systems.