An RFID antenna assembly is made by first adhering a continuous aluminum foil between 1 μm and 20 μm thick by an adhesive film to a front face of a mounting layer, then providing on a back face of the mounting layer a film of contact adhesive, and then releasably securing to the mounting-layer back face a backing strip. The foil and the mounting layer but not the backing strip are then punched through so as to punch out antennas from the foil and identical pieces from the mounting layer. Finally the foil and mounting layer are stripped from around the punched-out antennas on the backing strip to leave on the backing strip a row only of the punched-out antennas and the respective pieces of the mounting layer.