A container that is impermeable to microwaves and is arranged in the cooking space of a microwave oven is allocated to an ozone generator which has a UV emitter suitable for generation of ozone. This UV emitter is fitted inside a chamber which is at least partially permeable to microwave radiation and whose interior is connected to the interior of the container via air passages. On operation of the microwave oven, the microwaves activate the UV emitter which in turn generates ozone which passes through the air passages into the container interior and sterilises the items to be sterilised and present therein.