A wireless electronic device may be provided with components such as electrical and structural components. During transmission of radio-frequency signals, antennas and wireless communications circuitry of the wireless electronic device may produce associated time-varying magnetic fields. One or more components may be covered with magnetic-resistant shield structures that protect the components from the time-varying magnetic fields by preventing magnetic-induced vibrations. The magnetic-resistant shield structures may include a conductive base layer such a layer of brass. A magnetic-resistant layer may be plated onto the conductive base layer. The magnetic-resistant layer may be formed from an amorphous nickel-phosphorous alloy. The amorphous nickel-phosphorous alloy may be produced by controlling the manufacturing temperature and proportion of phosphorous in the alloy while performing the plating operations within a length of time that ensures non-equilibrium conditions during the plating operations.