The superheating magnetic field of a Type II superconductor is examined using the time-dependent Ginzburg-Landau equations and the methods of formal asymptotics. The superconducting solution in a halfspace is found to exist only for magnetic fields lower than some critical value, where there is a folding over of the solution branch. A linear stability analysis is performed both in one and two dimensions, giving differing criteria for stability. Finally, superheating fields for more general geometries are considered and in particular the case of a sine-wave perturbation of a halfspace is examined.