Whispering gallery modes in high permittivity right cylindrical dielectric resonators are shown to be very useful at millimetre wavelengths since they offer a highQfactor and their oversized dimensions make them easy to manufacture. Using a dielectric waveguide model, simple expressions are generated that accurately predict the resonant frequencies of the WGE whispering gallery modes within right cylindrical dielectric resonators placed on a dielectric integrated circuit substrate of lower permittivity. Theoretical and experimental results are given and the accuracy of the proposed model is shown to be good.