Electrical components such as integrated circuits may be mounted on a printed circuit board. To prevent the electrical components from being subjected to electromagnetic interference, radio-frequency shielding structures may be formed over the components. The radio-frequency shielding structures may be formed from a layer of metallic paint. Components may be covered by a layer of dielectric. Channels may be formed in the dielectric between blocks of circuitry. The metallic paint may be used to coat the surfaces of the dielectric and to fill the channels. Openings may be formed in the surface of the metallic paint to separate radio-frequency shields from each other. Conductive traces on the surface of the printed circuit board may be used in connecting the metallic paint layer to internal printed circuit board traces.