Limestone is a widely used building material. Its degradation process is strongly linked to the water content, to which the radar waves are sensitive. In this paper, a model of stepped-frequency radar (SFR) wave propagation through partially wet limestone is proposed, in order to study the water transfer front in limestone. We assume the limestone as a two-layer (dry/wet) lossy medium and use an analytical model which combines Lambot's closed-form antenna model with zero-offset single-point Green's function and Jonscher's medium property model to describe the SFR wave propagation. It takes into account the frequency-dependence of dielectric properties using a frequency power law. We validate this model using a numerical verification platform based on HFSS, which is a commercial finite element method solver for electromagnetic structures. The frequency dependent complex permittivities coming from coaxial transmission line experiments are converted to the input of our analytical model and that of HFSS. The comparison on return loss S11 shows that the correspondence is very good, thus demonstrating the performance of this proposed model, which takes into account the effect of material dispersion.