Electronic devices may be provided with antenna structures. The antenna structures may be used in wirelessly transmitting and receiving radio-frequency signals. Antenna structures may be formed from molded dielectric substrates. Patterned conductive material may be formed on the dielectric substrates. The dielectric substrates may be formed from molded materials such as glass or ceramic. Sheets of dielectric or dielectric powder may be compressed to form a dielectric substrate of a desired shape. The patterned conductive material may be formed from metallic paint or other conductors. A hollow antenna chamber may be formed by joining molded dielectric structures. An antenna such as an indirectly-fed loop antenna or other antennas may be formed from the molded dielectric substrates and patterned conductors.