The paper discusses measurements of the relative permittivity and the loss angle (tan δ) of a material using the resonance method. The resonator used was a cylindrical cavity in which the dominant-mode excitation was H_01ν. The cross-section of each sample had a radius equal to the internal radius of the cavity, and the measurements were made with sample thicknesses ranging from one wavelength to a small fraction of a wavelength. Using circular coupling holes in the top surface of the cavity of the type described by Bleaney,² it was found that, over the range of sample thicknesses considered, the measured permittivity and tan δ showed a periodic variation, the total spread being 2% and 42%, respectively. Theoretical analysis shows that this particular type of coupling also excites the degenerate E_11νmode, and this accounts, at least partially, for the measured variation in the parameters of the material. An alternative type of coupling, through small slots cut in the curved sides of the cavity, is described, and this should give better discrimination against the E_11νmode and lead to measurements which are less dependent on the sample thickness. Experiments are described which bear this out, and variations in the measurements using the new coupling arrangement show, for the same sample-thickness range, a spread in permittivity and tan δ of 0.2 and 12%, respectively.