Antenna window structures and antennas are provided for electronic devices. The electronic devices may be laptop computers or other devices that have conductive housings. Antenna windows can be formed from dielectric members. The dielectric members can have elastomeric properties. An antenna may be mounted inside a conductive housing beneath a dielectric member. The antenna can be formed from a parallel plate waveguide structure. The parallel plate waveguide structure may have a ground plate and a radiator plate and may have dielectric material between the ground and radiator plates. The ground plate can have a primary ground plate portion and a ground strip. The ground strip may reflect radio-frequency signals so that they travel through the dielectric member. The antenna may handle radio-frequency antenna signals in one or more communications bands. The radio-frequency antenna signals pass through the dielectric member.