"Core/shell" nanocomposites based on magnetic magnetite (Fe3O4) and redox-active cerium dioxide (CeO2) nanoparticles (NPs) are promising in the field of biomedical interests because they can combine the ability of magnetic NPs to heat up in an alternating magnetic field (AMF) with the pronounced antioxidant activity of CeO2 NPs. Thus, this report is devoted to Fe3O4/CeO2 nanocomposites (NCPs) synthesized by precipitation of the computed amount of "CeO2-shell" on the surface of prefabricated Fe3O4 NPs. The X-ray diffraction, X-ray photoelectron spectroscopy, and high-resolution transmission electron microscopy data validated the formation of Fe3O4/CeO2 "core/shell"-like NCPs, in which ultrafine CeO2 NPs with an average size of approximately 3-3.5 nm neatly surround Fe3O4 NPs. The presence of a CeO2 "shell" significantly increased the stability of Fe3O4/CeO2 NCPs in aqueous suspensions: Fe3O4/CeO2 NCPs with "shell thicknesses" of 5 and 7 nm formed highly stable magnetic fluids with ζ-potential values of >+30 mV. The magnetization values of Fe3O4/CeO2 NCPs decreased with a growing CeO2 "shell" around the magnetic NPs; however, the resulting composites retained the ability to heat efficiently in an AMF. The presence of a CeO2 "shell" generates a possibility to precisely regulate tuning of the maximum heating temperature of magnetic NCPs in the 42-50 °C range and stabilize it after a certain time of exposure to an AMF by changing the thickness of the "CeO2-shell". A great improvement was observed in both antioxidant and antiamyloidogenic activities. It was found that inhibition of insulin amyloid formation, expressed in IC50 concentration, using NCPs with a "shell thickness" of 7 nm was approximately 10 times lower compared to that of pure CeO2. For these NCPs, more than 2 times higher superoxide dismutase-like activity was observed. The coupling of both Fe3O4 and CeO2 results in higher bioactivity than either of them individually, probably due to a synergistic catalytic mechanism.