A method of closing a packaging tray comprises arranging a packaging tray between a lower tool and an upper tool of a sealing station, positioning a cover film above the packaging tray between the lower tool and the upper tool, and pressing together the cover film and the packaging tray by a lower sealing surface of the lower tool and an upper sealing surface of the upper tool cooperating with the lower sealing surface. During the pressing together, a connection is established between the cover film and the packaging tray along a sealing seam. While the cover film and the packaging tray are being pressed together, an overpressure is locally generated by supplying pressurized gas from a pressurized-gas source, the overpressure cooperating as a counterpressure with the lower sealing surface or with the upper sealing surface so as to press the cover film and the packaging tray together.