An electromagnetically reflective plate for a miniature antenna device includes: etched conductive elements on a first dielectric substrate layer; an apertured ground plane placed between the first substrate layer and a second dielectric substrate layer; a set of metal through-vias formed in the thickness of the two substrate layers, each including an upper end making contact with one of the conductive elements, a lower end reaching a lower face of the second substrate layer, and passing through the ground plane without electrical contact in one of its apertures. Each conductive element makes contact with a plurality of vias and each via of each conductive element is connectable to another via of a neighboring conductive element using a corresponding electrical connection making contact with the lower end of this via. At least some of the electrical connections include one or more meanders.