A novel interaction cavity has been designed for a gyrotron, realising co-harmonic generation at the 2nd and 4th harmonic resonances of the electron cyclotron frequency. The output aperture of the cavity has been designed to trap the lower harmonic, whilst allowing output of the upper harmonic. Results from recent numerical simulations, performed using MAGIC 3-D, are presented. The intended co-harmonic behaviour is observed, with simultaneous excitation of the 2nd and 4th harmonics. Results are presented of a refinement of the output structure undertaken with CST Microwave Studio, to ensure that only the 4th harmonic signal is emitted.