Abstract: An oven or cooking appliance having a baking or oven compartment which can be heated by circulating air and can be furnished with microwaves by means of a microwave generator. At the underside of the microwave generator, in spaced relationship from the ceiling of the oven compartment, there is provided a heat shield or screen. A waveguide which is leakproof for microwaves and substantially hermetically sealed against the oven compartment but permeable to microwaves in the direction of the oven compartment is provided with air permeable walls. Blower means feed cooling air between the heat shield and the ceiling of the oven compartment and through the waveguide.