A relatively simple technique for measuring the effective ferromagnetic resonance linewidth Delta H_eff of microwave ferrites is described. The experimental set-up consists of standard available waveguide components. The frequency of a klystron generator is stabilised by a cavity wavemeter, using a moderate-gain feedback DC amplifier. The spherical sample to be measured is placed in the centre of a rectangular H₁₀₂ cavity. The resonance frequency shift is determined by the repeller voltage variation necessary to retune the cavity in resonance, while the change of reciprocal Q is calculated from the additional cavity attenuation caused by the sample. A modification of the arrangement suitable for measuring the permittivity of cylindrical samples in a rectangular H₁₀₃ cavity is also described. A comprehensive analysis of measurement errors is presented. The estimated inaccuracy of Delta H_eff is in most cases about 10%, while the errors of real permittivity and loss tangent are less than 3% and 20%, respectively, for loss tangents down to 2*10^-4.