We study the effect of the substrate on the effective surface impedance of a YBa2Cu3O7-delta thin film grown over a silicon substrate. The microwave measurements, performed with a resonant cavity technique at two distinct frequencies (24 and 48 GHz), show anomalies both in the temperature and in the frequency dependences. By properly taking into account a relevant complex substrate contribution, with an important role played by the finite thickness effect, the whole set of data finds a satisfactory explanation in terms of standard impedance transformations. Using independent measurements at a single temperature, it is possible to extract the temperature dependence of the YBa2Cu3O7-delta bulk surface impedance, which shows the expected frequency and temperature behaviours.