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The use of ground-penetrating radar (GPR) techniques at high frequencies for historical building investigations requires an accurate knowledge of the material complex permittivity. A new measurement system is presented, which by exploiting a resonance phenomenon, yields accurate values of permittivity and resistivity also in the case of low-loss materials. These parameters are obtained from an amplitude-only measurement of the transmission response curve of a rectangular waveguide cavity, loaded by the sample under test. The setup requires the availability of brick-shaped samples, which can be obtained easily in the case of rock materials. Permittivities and resistivities were measured in the frequency range 1.1-1.7 GHz on samples of marbles, sandstones, and limestones. The measurement method and the experimental results are presented and discussed.