Electronic devices such as computers and handheld devices are provided. The electronic devices may have electrical components such as displays that are driven by driver circuitry. During operation, the driver circuitry may generate radio-frequency noise. Communications circuitry in the electronic devices may be shielded from the radio-frequency noise by radio-frequency shielding structures. The shielding structures may be mounted on portions of the display module, on a cover glass layer, or on other structures such as housing structures. The radio-frequency shielding structures may be formed from one or more metal segments. The metal segments may run along edges of the display. A device housing may have a ground formed from a conductive peripheral member that runs around peripheral edges of the housing and a conductive plate that is connected to the conductive peripheral member. The radio-frequency shielding structure may be connected to the ground using conductive structures.