Ovenware for microwave ovens which contain a composition comprising a susceptor and a thermoplastic or thermoset polymer are improved when the composition also has a thermal conductivity of about 0.7 W/m°K or more. Heat generated by absorption of microwave radiation by the susceptor is more readily conducted to the food being cooked when the thermal conductivity of the composition is high, particularly when the part containing the susceptor is relatively thick. Also described are designs for various pieces of ovenware containing this composition.