The present work investigates whether dielectric spectroscopy can be used to detect contamination, which may leach in a natural porous material, due to the spreading of contaminants. For this purpose, dielectric and conductivity measurements, in the frequency range from 10 mHz to 1 MHz, were carried out in sandstone samples, partially filled or saturated with solutions of leachates, at different concentrations. The experimental results suggest the dominant role of free water to the measured electrical conductivity and dielectric permittivity in contaminated samples with high water content. On the other hand, various relaxation mechanisms were observed in dried samples at different leachate concentrations. Experimental data were fitted using the Havriliak–Negami dielectric relaxation function, superimposed with a conductivity term. The determined parameters of the fitting function may serve to distinguish between different amounts of leachate in sandstone samples.