A one step general synthetic methodology for the synthesis of 6-aryl-5,6-dihydropyrido[2,3-d]pyrimidine-4,7(3H,8H)-diones (17{[Formula: see text]} ([Formula: see text]) and 20{[Formula: see text]} ([Formula: see text])) is described. This methodology is based on reacting a 2-aryl-substituted acrylate (16{[Formula: see text]}) with the corresponding 6-aminopyrimidin-4(3[Formula: see text]-one (13 ([Formula: see text]; 19 ([Formula: see text])) in presence of a base under microwave irradiation. The resulting pyrido[2,3-[Formula: see text]]pyrimidines present an aryl substituent at position C6, precisely the one directly related to the biological activity of such heterocycles. These protocols have been extended to other 2-alkyl-substituted and 3-alkyl (or aryl)-substituted acrylates but with lower yields.