A co-harmonic gyrotron, operating simultaneously at the second and fourth harmonics of the electron cyclotron frequency, has been successfully modelled with the particle-in-cell code, Magic 3D. Results show excitation of the TE 2,2 and TE 4,3 waveguide modes, at frequencies of 37.5GHz and 75GHz, respectively, consistent with experimental measurements. The total predicted output power was 3kW. Lengthening of the cut-off output taper has demonstrated an improved confinement of the second harmonic signal, facilitating purer output of the fourth harmonic signal. In this enhanced configuration, the predicted output power of the second harmonic was 250W, while the fourth harmonic was 15W. The system demonstrates the potential for selective fourth harmonic generation, for starting currents which are two orders of magnitude lower than would be required for direct excitation.