Described are ways of improving the yields of specification grade polyimide foam on a consistent basis from one run to the next by use of improvements in microwave-based foaming processes. While a body of polyimide precursor is exposed to microwave radiation, the body of polyimide precursor and of the foam structure as it is developing therefrom are kept under a substantially vapor-impermeable microwave-compatible shroud that does not substantially restrict or impede development of the foam structure. For this purpose use may be made of a shroud composed of a polymer film. Mechanisms by which the shroud produces the improved results are discussed, and methods based thereon are set forth.