Electronic devices may be provided with antenna structures. The antenna structures may include an antenna support structure covered with patterned antenna traces. An antenna support structure may be mounted in an electronic device so that a surface of the antenna support structure that is covered with patterned antenna traces lies flush with a planar surface of the electronic device housing. A display cover layer or other planar structure may be attached to the surface of the antenna support structure and the planar surface of the housing adhesive. Injection molding and extrusion techniques may be used in forming a support structure with elongated parallel cavities. An injection molding tool may have a mold core supported by a support structure at one end, supporting engagement features at the ends of mating mold core structures, or support pins. Molded interconnect devices may be soldered to laser direct structuring components to form antennas.