A method for assembling and hermetically sealing a package consisting of a side wall mounted on, or integral with a substrate, with the space thus defined accommodating at least one component that operates in a vacuum or at reduced pressure or, more generally, in a controlled atmosphere, said space being closed off by a hermetic sealing cover (5, 41-43) sealed on said side wall, with this method involving: - providing in the side wall at least one opening or recess in the vicinity of its upper edge, said opening or recess being capable of accommodating a functional element mounted so that it overhangs, said functional element being shaped accordingly; - fitting said functional element within said recess, said functional element being provided with at least one protrusion or protuberance (17, 18) capable of being accommodated in the opening or recess, the center of gravity of said functional element being offset outside the support perimeter defined by area of said protrusion or protuberance (17, 18) which cooperates with the recess or opening, so that the functional element is capable of swiveling from a non-operational position to an operational position when positioning the upper cover on the upper face of the side wall; - depositing a metallic connector element, also referred to as a brazing preform, onto the upper face of the side wall; - depositing the upper cover (41 - 43) on, and in contact with, said brazing preform, thereby causing cooperation of said functional element with the brazing preform and, consequently, positioning of the functional element in accordance with its operating mode; - subjecting the assembly thus obtained to the desired environment in terms of the kind of gas and operating pressure of the component; - increasing the temperature to a value that is at least in excess of the melting temperature of the material that constitutes the brazing preform; - then lowering said temperature in order to cause solidification of said brazing material and, consequently, sealing of the upper cover on the side wall. - providing in the side wall at least one opening or recess in the vicinity of its upper edge, said opening or recess being capable of accommodating a functional element mounted so that it overhangs, said functional element being shaped accordingly; - fitting said functional element within said recess, said functional element being provided with at least one protrusion or protuberance (17, 18) capable of being accommodated in the opening or recess, the center of gravity of said functional element being offset outside the support perimeter defined by area of said protrusion or protuberance (17, 18) which cooperates with the recess or opening, so that the functional element is capable of swiveling from a non-operational position to an operational position when positioning the upper cover on the upper face of the side wall; - depositing a metallic connector element, also referred to as a brazing preform, onto the upper face of the side wall; - depositing the upper cover (41 - 43) on, and in contact with, said brazing preform, thereby causing cooperation of said functional element with the brazing preform and, consequently, positioning of the functional element in accordance with its operating mode; - subjecting the assembly thus obtained to the desired environment in terms of the kind of gas and operating pressure of the component; - increasing the temperature to a value that is at least in excess of the melting temperature of the material that constitutes the brazing preform; - then lowering said temperature in order to cause solidification of said brazing material and, consequently, sealing of the upper cover on the side wall.