The dielectric response of thin films of perovskite ferroelectrics fabricated on electrodes such as indium tin oxide is calculated as a function of frequency, film & barrier layer thickness, and dielectric constant using an equivalent circuit model based on properties of the bulk, the electrode and a series resistance. Using reasonable estimates of parameters it is shown that measurements of the dielectric constant and loss by conventional dielectric bridges can lead to results which vary in a complex fashion and which may bear little relation to the true dielectric properties of the film. In particular, observation of a Curie temperature in thin films can often be masked by circuit or electrode effects. Results are given in terms of direct frequency plots and as impedance spectra.