Abstract: 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 improved microwave-based foaming processes. In one such process, during the application of the microwave radiation, the body of polyimide precursor and of the foam structure as it is developing therefrom are maintained under a substantially vapor-impermeable mmicrowave-compatible shroud that does not substantially restrict or impede development of the foam structure; and the microwave radiation is directed upon the top, sides and ends of the body of polyimide precursor and of the foam structure as it is developing, but the extent to which such radiation impinges upwardly into the bottom of said body and said foam structure is curtailed, preferably by means of a metallic shield located below the precursor and developing foam structure.