This paper describes an efficient algorithm to predict the RF gas breakdown power threshold in microwave devices with complex geometries. The two necessary calculations when investigating such a phenomenon have been performed: on the one hand, the computation of the electromagnetic fields inside the structure and, on the other hand, the determination of the breakdown onset itself. The electromagnetic fields are solved by means of modal techniques and coupled to the free electron continuity equation, which is solved by the Finite Element Method. Proceeding in this way, a very simple criterion to find out whether microwave corona breakdown will take place is derived. This numerical implementation of the developed algorithms has been tested with other theoretical approaches and with experimental measurements, showing very good agreement.