Indium-substituted strontium hexaferrites were prepared by the conventional solid-phase reaction method. Neutron diffraction patterns were obtained at room temperature and analyzed using the Rietveld methods. A linear dependence of the unit cell parameters is found. In3+ cations are located mainly in octahedral positions of 4fVI and 12 k. The average crystallite size varies within 0.84–0.65 μm. With increasing substitution, the TC Curie temperature decreases monotonically down to ~ 520 K. ZFC and FC measurements showed a frustrated state. Upon substitution, the average and maximum sizes of ferrimagnetic clusters change in the opposite direction. The Mr remanent magnetization decreases down to ~ 20.2 emu/g at room temperature. The Ms spontaneous magnetization and the keff effective magnetocrystalline anisotropy constant are determined. With increasing substitution, the maximum of the ε/ real part of permittivity decreases in magnitude from ~ 3.3 to ~ 1.9 and shifts towards low frequencies from ~ 45.5 GHz to ~ 37.4 GHz. The maximum of the tg(α) dielectric loss tangent decreases from ~ 1.0 to ~ 0.7 and shifts towards low frequencies from ~ 40.6 GHz to ~ 37.3 GHz. The low-frequency maximum of the μ/ real part of permeability decreases from ~ 1.8 to ~ 0.9 and slightly shifts towards high frequencies up to ~ 34.7 GHz. The maximum of the tg(δ) magnetic loss tangent decreases from ~ 0.7 to ~ 0.5 and shifts slightly towards low frequencies from ~ 40.5 GHz to ~ 37.7 GHz. The discussion of microwave properties is based on the saturation magnetization, natural ferromagnetic resonance and dielectric polarization types.