A measuring system for determining the complex permittivity of low-loss solids using a frequencytuned TE01cavity resonator of fixed length is described. Its mechanical construction is simple, and measurements, in particular of the real part ε' of the permittivity, can be performed within a relatively short measuring time with high precision ($$$δε'/ε'|< 7 × 10−4), for a large number of frequencies in a given frequency band. The method is compared with the standard method where a length-tuned resonator is involved. Theoretical error investigations and practical measurements at frequencies of about 10 GHz on polymers and fused silica are carried out showing that the uncertainties have comparable values in both methods.