The structure of high Mach number perpendicular shocks is examined using a simulation code which treats the ions as macroparticles and the electrons as a resistive massless fluid. It is shown that stable, stationary shock solutions can be found for Alfv¿n Mach numbers MA between 5 and 60 for upstream plasma &bgr;=1, where &bgr; is defined as the ratio of the plasma pressure to the magnetic pressure, provided that the upstream resistive diffusion length is much smaller than the ion inertial length c/wpi. If the resistive diffusion length is larger than 0.4c/wpdi, then the magnetic field overshoot is damped, and an imbalance in the electron momentum equation results in a periodic fluctuation of the fraction of reflected ions. In the limit MA≤10, the magnetic field overshoot and the fraction of reflected ions increase with increasing MA, consistent with earlier results. At higher Mach numbers the fraction of reflected ions peaks at approximately 40% and the magnetic field overshoot increases at a much slower rate. These results are consistent with simple scaling laws derived from the electron momentum equation. The importance of upstream &bgr; and electron inertial effects are discussed.