Electrical components may be shielded using a shielding can or other shielding structure that covers the electrical components. The electrical components and the shielding structure may be mounted on a substrate such as a printed circuit board using solder or other conductive material. The shielding structure may have one or more shielding layers. The shielding layers may include high conductivity material for providing shielding for radio-frequency electromagnetic interference and magnetic material for blocking magnetic flux. Shielding structures may be formed from materials such as ferritic stainless steel, coatings that enhance solderability, corrosion resistance, and conductivity, magnetic materials printed or otherwise formed on metal layers, and other shielding structures.