We have studied dielectric and magnetic losses in granular structures constituted by ferromagnetic nanoparticles (Co, Fe, B) in an insulating amorphous a-SiO₂ matrix at microwave frequencies, in relation to metal concentration, substrate temperatures and gas content, in the plasma atmosphere in sputtering and annealing. The magnetic losses are due to fast spin relaxation of nanoparticles, which becomes more pronounced with decreasing metal content and occur via simultaneous changes in the granule spin direction and spin polarization of electrons on exchange-split localized states in the matrix (spin-polarized relaxation mechanism). The difference between the experimental values of the imaginary parts of magnetic permeability for granular structures prepared in Ar and Ar + O₂ atmospheres is determined by different electron structures of argon and oxygen impurities in the matrix. To account for large dielectric losses in granular structures, we have developed a model of cluster electron states (CESs). Cluster states are formed by s-electrons of nanoparticles and by electrons in localized states in intergranule regions of the matrix. The observed sharp increase in dielectric losses in the percolation region, the different values of losses for structures sputtered in the Ar and Ar + O₂ atmospheres and reduction of dielectric losses upon annealing, are caused by electric dipole polarization of electrons in CESs.