Employing a (1+1)-dimensional model, we discuss non-perturbative methods for the description of the ionization of highly excited hydrogen atoms by a pulsed strong microwave field. We restrict our attention to high scaled frequenciesn3ω≧1 and show that the recently developed picture of Landau-Zener dynamics leads to a transparent explanation of prominent structures in the 10% ionization curve measured by Koch et al. in experiments using microwave cavities; these structures are predicted to depend on fringe field parameters in a systematic manner. Waveguide experiments are expected to yield qualitatively different results.