A shielded substrate assembly that contains a magnetic shield with a layer of magnetic shielding material; the magnetic shield has a magnetic shielding factor of at least about 0.5. The magnetic shield contains nanomagnetic material nanomagnetic material with a mass density of at least about 0.01 grams per cubic centimeter, a saturation magnetization of from about 1 to about 36,000 Gauss, a coercive force of from about 0.01 to about 5,000 Oersteds, a relative magnetic permeability of from about 1 to about 500,000, and an average particle size of less than about 100 nanometers. The nanomagnetic material contains magnetic material with a coherence length of from about 0.1 to about 100 nanometers.