The inverse problem of reconstructing the real permittivity of a plane-parallel layer in a perfectly conducting rectangular waveguide from experimental data using an explicit expression for the scattering matrix is considered. This problem is ill-posed due to the presence of self-intersection points on the curves of the complex scattering coefficients. It is shown that the traditional multi-frequency measurement method used in vector network analyzers can be justified by the fact that the algorithm for processing the measurement results by the least squares method becomes stable if the number of frequencies is large enough.