Summary: The microwave heating of a material with temperature-dependent, nonohmic conductance is considered both analytically and numerically. In the case when the microwave amplitude is small, it is shown using a multiple scales expansion that the heating is governed by a Ginzburg-Landau type equation. This equation does not possess the solitary wave solutions of the full Ginzburg-Landau equation. Approximate solutions in the form of a slowly varying soliton and a front are found in certain parameter limits; these solutions compare very well with numerical solutions of the full governing equations. Initial-boundary value and initial value problems are considered numerically with particular emphasis on the structure of fronts.