Physical drift and diffusion simulations were performed in order to optimise the device structure of and to understand the relevant physical processes in 4H-SiC microwave power MESFETs. The doping and thickness of the channel and buffer layers were optimised. The maximum drain current was above 300 mA/mm. The optimum power performance was modelled using both DC and RF analysis. The cut-off and the maximum frequency of oscillation for a device with a gate length 0.5 mum were 13 and 45 GHz respectively. The maximum achievable gain was above 10 dB up to 26 GHz. The Self-heating due to current flow in the device was modelled and the channel temperature was as high as 636 K at a drain bias of 130 V.