An antenna device comprising: - a first substrate, extending in a first plane, having at least one face on which are formed: • at least one radio antenna (20, 22) extending into a first radiating portion of the first substrate, and • electrically conductive means (24, 26, 28) for connecting said at least one radio antenna (20, 22) to an electronic transmitter and/or receiver circuit, said electrically conductive means (24, 26, 28) extending in a second portion of the first substrate, - a second substrate extending in a second plane different from and intersecting the first plane, separating the first radiating portion of the first substrate, located in a first half-space with respect to this second plane, from the second portion of the first substrate, located in a second half-space with respect to this second plane, the second substrate having a face, referred to as the lower face and oriented on the side of said second half-space in which the electrically conductive connection means (24, 26, 28) are located, comprising a metamaterial structure with multiple electrically conductive elements electrically separated from one another on this lower face, said at least one radio antenna (20, 22) being at least one printed antenna extending over at least one face of the first substrate, said at least one radio antenna comprising a first low-frequency printed antenna operating in a first band of electromagnetic frequencies and a second high-frequency printed antenna operating in a second band of electromagnetic frequencies all higher than the electromagnetic frequencies of the first band of frequencies the second substrate comprising: - a metallic ground plane extending on another face, called the upper face and opposite the lower face comprising the metamaterial structure, and - through vias connecting each electrically conductive element of the metamaterial structure to the metal ground plane. - a first substrate, extending in a first plane, having at least one face on which are formed: • at least one radio antenna (20, 22) extending into a first radiating portion of the first substrate, and • electrically conductive means (24, 26, 28) for connecting said at least one radio antenna (20, 22) to an electronic transmitter and/or receiver circuit, said electrically conductive means (24, 26, 28) extending in a second portion of the first substrate, • at least one radio antenna (20, 22) extending into a first radiating portion of the first substrate, and • electrically conductive means (24, 26, 28) for connecting said at least one radio antenna (20, 22) to an electronic transmitter and/or receiver circuit, said electrically conductive means (24, 26, 28) extending in a second portion of the first substrate, - a second substrate extending in a second plane different from and intersecting the first plane, separating the first radiating portion of the first substrate, located in a first half-space with respect to this second plane, from the second portion of the first substrate, located in a second half-space with respect to this second plane, the second substrate having a face, referred to as the lower face and oriented on the side of said second half-space in which the electrically conductive connection means (24, 26, 28) are located, comprising a metamaterial structure with multiple electrically conductive elements electrically separated from one another on this lower face, said at least one radio antenna (20, 22) being at least one printed antenna extending over at least one face of the first substrate, said at least one radio antenna comprising a first low-frequency printed antenna operating in a first band of electromagnetic frequencies and a second high-frequency printed antenna operating in a second band of electromagnetic frequencies all higher than the electromagnetic frequencies of the first band of frequencies the second substrate comprising: - a metallic ground plane extending on another face, called the upper face and opposite the lower face comprising the metamaterial structure, and - through vias connecting each electrically conductive element of the metamaterial structure to the metal ground plane. - a metallic ground plane extending on another face, called the upper face and opposite the lower face comprising the metamaterial structure, and - through vias connecting each electrically conductive element of the metamaterial structure to the metal ground plane.