An electronic device such as a computer monitor is provided that has an antenna that supports near field communications. The electronic device may have a housing with conductive housing surfaces. A display may be mounted in the housing. The conductive housing surfaces may contain a dielectric-filled hole. The antenna may have a substrate and one or more loops of conductive traces. The loops may exhibit mirror symmetry. The loops may overlap the display and the conductive housing surface. The loops may surround an inner loop-free portion of the antenna. The loop-free portion of the antenna may overlap the hole. Ferrite layers may be interposed between the loops of the antenna that overlap the display and the loops of the antenna that overlap the conductive housing.