The presence of ferromagnetic or ferrimagnetic nanoparticles in the interstellar medium would give rise to magnetic dipole radiation at microwave and submillimeter frequencies. Such grains may account for the strong millimeter-wavelength emission observed from a number of low-metallicity galaxies, including the Small Magellanic Cloud. We calculate the absorption and scattering cross sections for such grains, with particular attention to metallic Fe, magnetite Fe sub(3)O sub(4), and maghemite gamma -Fe sub(2)O sub(3), all potentially present in the interstellar medium. The rate of Davis-Greenstein alignment by magnetic dissipation is also estimated. We determine the temperature of free-flying magnetic grains heated by starlight and calculate the polarization of the magnetic dipole emission from both free-fliers and inclusions. For inclusions, the magnetic dipole emission is expected to be polarized orthogonally relative to the normal electric dipole radiation. Magnetic dipole radiation will contribute significantly to the 20-40 GHz anomalous microwave emission only if a large fraction of the Fe is in metallic Fe iron nanoparticles with extreme elongations. Finally, we present self-consistent dielectric functions for metallic Fe, magnetite Fe sub(3)O sub(4), and maghemite gamma -Fe sub(2)O sub(3), enabling calculation of absorption and scattering cross sections from microwave to X-ray wavelengths.