An electronic device may have a display. A display cover layer and a transparent inner display member may overlap a display pixel layer. The display pixel layer may have an array of display pixels for displaying images for a user. A touch sensor layer may be interposed between the display pixel layer and the transparent display member. A ferromagnetic shielding layer may be mounted below the display pixel layer. A flexible printed circuit containing coils of metal signal lines that form a near-field communications loop antenna may be interposed between the ferromagnetic shielding layer and the display pixel layer. A non-near-field antenna such as an inverted-F antenna may have a resonating element mounted on an inner surface of the display cover layer. The resonating element may be interposed between the transparent display member and the display cover layer.