Four types of magnetic nanoparticles were synthesized, namely, the La0.65Sr0.35MnO3 and La0.80Na0.20MnO3 perovskite manganites and the Mn0.61Zn0.42Fe1.97O3 and Co0.44Zn0.70Fe1.86O4 spinel ferrites. Subsequent coating with silica provided typical core-shell particles with the mean shell thickness of 14-19 nm and the mean size of cores of 49-52 nm in the case of manganites and 26-33 nm in the case of ferrites. Moreover, two other surface modifications were employed for Mn-Zn ferrite nanoparticles, specifically coating with titania, leading to larger clusters with more complex morphology, and the stabilization by citrate anions. The products were characterized by powder X-ray diffraction and transmission electron microscopy, and their magnetic properties were probed by SQUID magnetometry. The main attention was devoted to the relaxometry on aqueous suspensions of particles in a magnetic field of 0.5 T. For distinct types of the prepared core-shell nanoparticles, the temperature dependence of transverse relaxivity was measured and the role of different relaxation regimes was analyzed.