An electronic device may have a housing with conductive housing walls. A dielectric antenna window may be formed in an opening in one of the conductive housing walls. A dielectric logo may form the dielectric antenna window. A dielectric support structure may have an outline that matches the dielectric logo. An antenna resonating element for an antenna may be formed on the dielectric support structure. An antenna cavity for the antenna may be formed by a conductive cavity structure. A pattern of voids in the dielectric support structure may reduce dielectric loading for the antenna. The conductive cavity structure may be formed from solderable plated metal. The conductive cavity structure may have a planar lip that is attached to the conductive housing walls using conductive adhesive. Rear wall portions of the conductive cavity structure may be oriented at a non-perpendicular non-zero angle with respect to the planar lip.