A model coupling Maxwell's equations with electron fluid equations is used to simulate air and SF 6 breakdown at high pressure by microwaves radiated from a circular waveguide. The modeling for microwaves radiated from a circular waveguide is validated by comparing its results with those from the commercial software FEKO. Under a fixed initial growth rate of electron density in the maximum radiated field, the space and time evolution of electron density in SF 6 breakdown is similar to that in air breakdown. However, SF 6 plasma causes less change in the radiated field than air plasma. This is because the saturation electron density playing an important role in absorption and scattering by plasma is lower in SF 6 than in air. The ratio of critical radiated power in SF 6 to that in air increases as pulsewidth or gas pressure increases. The breakdown threshold from simulations as a function of pressure shows the same trend as the experiment.