Molded air cavity packages and methods for producing molded air cavity packages are disclosed. In one embodiment, the molded air cavity package includes a molded package body having an upper peripheral edge portion, an air cavity around which the upper peripheral edge portion extends, and a cover piece bonded to the upper peripheral edge portion to enclose the air cavity. The cover piece has a lower peripheral edge portion, which cooperates with the upper peripheral edge portion to define a cover-body interface. The cover-body interface includes an annular channel extending around the cover-body interface, as taken about the package centerline, and first and second hardstop features formed on the upper peripheral edge portion of the molded package body and on the lower peripheral edge portion of the cover piece, respectively. The hardstop features contact to determine a vertical height of the annular channel, as taken along the package centerline.