Electronic components on a substrate may be shielded using electromagnetic shielding structures. Insulating materials may be used to provide structural support and to help prevent electrical shorting between conductive materials and the components. The shielding structures may include compartments formed using metal fences that surround selected components or by injection molding plastic. The shielding structures may be formed using metal foil wrapped over the components and the substrate. Electronic components may be tested using test posts or traces to identify components that are faulty. The test posts or traces may be deposited on the substrate and may be used to convey test signals between test equipment and the components. After successful testing, the test posts may be permanently shielded. Alternatively, temporary shielding structures may be used to allow testing of individual components before an electronic device is fully assembled.