An electronic device may have a housing, electrical components, and other electronic device structures. A display may be mounted in the housing. The display may have a transparent display cover layer and a display layer such as an organic light-emitting diode display layer that is mounted to the underside of the transparent display cover layer. A flexible printed circuit with metal traces may be mounted under the organic light-emitting diode display layer. The metal traces may form coils for a near-field communications inductive loop antenna. A magnetic shielding layer may be interposed between the housing and the flexible printed circuit. The magnetic shielding layer may include a polymer magnetic shielding layer having magnetic material particles embedded in a polymer matrix. The magnetic shielding layer may also have a polymer-binder-free magnetic shielding layer.