A removable case may receive an electronic device. A male connector in the case may mate with a female connector in the device. A battery in the case may supply power to the device through the male connector. The electronic device may have an antenna formed from peripheral conductive housing structures and an antenna ground. The case may have a supplemental antenna that restores antenna performance when the device is received within the case. The supplemental antenna may be formed from a monopole antenna resonating element coupled to the antenna ground through the power pin. The monopole element may have a portion that runs parallel to the peripheral conductive housing structures. During operation of the antenna in the electronic device, the supplemental antenna in the case may be indirectly fed by near-field coupling between the supplemental antenna and the antenna of the electronic device.