Polyanhydrides were synthesized from aliphatic and aromatic diacids using microwave radiation without vacuum at significantly reduced reaction times when compared to conventional melt polycondensation. Reaction conditions, such as duration of polymerization, equivalents of acetic anhydride, and choice of starting species, were studied. In addition, copolymers were synthesized and monomer sequence lengths were calculated using dyad conditional probabilities. The results are in good agreement with monomer sequence lengths from conventional copolymerization.