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 TE2,2 and TE4,3 waveguide modes, at frequencies of 37.5 GHz and 75 GHz, respectively, consistent with experimental measurements. The total predicted output power was ∼3 kW. 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 ∼250 W, while the fourth harmonic was ∼15 W. 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.