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It is demonstrated that microwave structures incorporating dielectric resonators (DR) are accurately characterised by means of a 3-dimensional finite-difference CAD package. All major assumptions made so far have been dropped, offering the possibility of a rigorous analysis of the embedding of dielectric resonators into microwave structures. In particular, a finite thickness for the microstrip conductor has been taken into account. The coupling of the DR to a microstrip placed in a metallic housing has been theoretically and experimentally investigated. Theoretical and experimental results are in good agreement and give new insight into DR coupling to microstrip circuits.