The invention provides a method for preparing a polyanhydride by irradiating one or more diacids with microwave radiation in the presence of a carboxylic anhydride so as to acylate the one or more diacids to yield at least one prepolymer, and irradiating the prepolymer with microwave radiation so as to polymerize said prepolymer to yield the polyanhydride, as a homopolymer or a copolymer. High purity polyanhydrides can be prepared by this method. Reaction times compared to conventional melt polycondensations can be significantly reduced. Copolymer polyanhydrides can also be prepared by the microware radiation techniques described herein.