Abstract We present studies on the changes of the dielectric properties of 0.7 – 1.2-mm thick-layers of Sr₃Co₂Fe₂₄O₄₁ Z-type hexaferrite in the frequency range 5 – 40 GHz; to the best of our knowledge, for the first time we used a combination of two methods – a resonance method, which yields infomation on the dielectric and magnetic anisotropies of the samples, and a broadband transmission-line method – covered coplanar and microstrip lines. We measured an increase of the dielectric constant and dielectric loss tangent above 20 GHz and a measurable anisotropy of the permittivity and permeability. The changes in the two parameters were also investigated (a magneto-electric effect was observed) in an external dc magnetic field in directions parallel and perpendicular to the sample at room temperature. The investigations presented are complex and intricate and should be considered as a first step in the characterization of thick Sr₃Co₂Fe₂₄O₄₁ Z-type hexaferrite slabs above 3 GHz up to the mm-wave range.