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, prior to the application of the microwave radiation, the body of polyimide precursor is compressed at a pressure that will reduce the bulk volume of the precursor and heated to a temperature below that at which any substantial foaming occurs. to accomplish the foaming, one further embodiment of the invention employs microwave radiation directed upon the top, sides and ends of the body of above-treated polyimide precursor and of the foam structure as it is developing maintaining the developing foam under a substantially vapor-impermeable microwave compatible shroud. The extent to which the microwave 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.