We propose a new swept-frequency measurement method for the electromagnetic characterization of materials. The material is a multilayer cylinder that pierces a rectangular waveguide through two holes in the narrow waveguide walls. The complex permittivity and permeability of the material are calculated from measured S-parameters as an inverse problem. To this aim, the paper develops a complete electromagnetic formulation of the problem, where the effects of material insertion holes are taken into consideration. The formulation is validated through the measurement of ferrite and water samples in the S-band.