Methods to produce substantially closed cell foams with densities less than 0.75 g/cm3, and more preferably less than 0.5 g/cm3, without substantial loss of the polymer's weight average molecular weight, have been developed. The closed cells foams have an open cell content of generally less than 50%, and more preferably an open cell content of less than 20%, and the cells have a maximum diameter of less than 5 mm. The foam may include poly-4-hydroxybutyrate or a copolymer thereof. Preferably, the foam is derived by heating a foam polymer formula to a temperature above the melt temperature of the polymer to form a melt polymer system, adding a blowing agent to produce a foamable melt, extruding the foamable melt through a die to a lower pressure to cause foaming, cooling of the foam, and solidification of the foam. These foam structures can be used for fabrication of medical products.