An electromagnetically reflective plate (10; 50) with a metamaterial structure for a miniature antenna device including: - a dielectric substrate having at least two dielectric substrate layers; - a plurality of conductive elements (20, 22, 24, 26) separated from each other and etched on an upper face of a first dielectric substrate layer, - a ground plane placed between a lower face of the first dielectric substrate layer and an upper face of a second dielectric substrate layer, with apertures arranged in this ground plane, - a set of metal through-vias formed in the thickness of the first and second substrate layers, each one including an upper end making contact with one of the conductive elements (20, 22, 24, 26), a lower end reaching a lower face of the second dielectric substrate layer, and passing through the ground plane without electrical contact in one of its apertures, wherein: - each conductive element (20, 22, 24, 26) makes contact with a plurality of metal vias (42; 42 a, 42 b, 42 c, 42 d), and - each metal via (42; 42 a, 42 b, 42 c, 42 d) of each conductive element is connectable to another metal via of a neighboring conductive element, using a corresponding electrical connection (46; 46 a, 46 b, 46 c, 46 d) making contact with the lower end of this metal via, characterized in that at least some of said electrical connections (46; 46 a, 46 b, 46 c, 46 d) has several meanders, wherein each electrical connection with meanders (46; 46 a, 46 b, 46 c, 46 d) is etched on the lower face of the second dielectric substrate layer and progressively expands from the end thereof making contact with the corresponding metal via (42; 42 a, 42 b, 42 c, 42 d) towards one of the edges of the conductive element (20, 22, 24, 26) under which it is etched. - a dielectric substrate having at least two dielectric substrate layers; - a plurality of conductive elements (20, 22, 24, 26) separated from each other and etched on an upper face of a first dielectric substrate layer, - a ground plane placed between a lower face of the first dielectric substrate layer and an upper face of a second dielectric substrate layer, with apertures arranged in this ground plane, - a set of metal through-vias formed in the thickness of the first and second substrate layers, each one including an upper end making contact with one of the conductive elements (20, 22, 24, 26), a lower end reaching a lower face of the second dielectric substrate layer, and passing through the ground plane without electrical contact in one of its apertures, wherein: - each conductive element (20, 22, 24, 26) makes contact with a plurality of metal vias (42; 42 a, 42 b, 42 c, 42 d), and - each metal via (42; 42 a, 42 b, 42 c, 42 d) of each conductive element is connectable to another metal via of a neighboring conductive element, using a corresponding electrical connection (46; 46 a, 46 b, 46 c, 46 d) making contact with the lower end of this metal via, characterized in that at least some of said electrical connections (46; 46 a, 46 b, 46 c, 46 d) has several meanders, wherein each electrical connection with meanders (46; 46 a, 46 b, 46 c, 46 d) is etched on the lower face of the second dielectric substrate layer and progressively expands from the end thereof making contact with the corresponding metal via (42; 42 a, 42 b, 42 c, 42 d) towards one of the edges of the conductive element (20, 22, 24, 26) under which it is etched. - each conductive element (20, 22, 24, 26) makes contact with a plurality of metal vias (42; 42 a, 42 b, 42 c, 42 d), and - each metal via (42; 42 a, 42 b, 42 c, 42 d) of each conductive element is connectable to another metal via of a neighboring conductive element, using a corresponding electrical connection (46; 46 a, 46 b, 46 c, 46 d) making contact with the lower end of this metal via, characterized in that at least some of said electrical connections (46; 46 a, 46 b, 46 c, 46 d) has several meanders, wherein each electrical connection with meanders (46; 46 a, 46 b, 46 c, 46 d) is etched on the lower face of the second dielectric substrate layer and progressively expands from the end thereof making contact with the corresponding metal via (42; 42 a, 42 b, 42 c, 42 d) towards one of the edges of the conductive element (20, 22, 24, 26) under which it is etched.