Cobalt-substituted ferrite nanoparticles with FCC structure have been synthesized using reverse micelles. Because the reverse micelles act as templates, we obtained nanoparticles with approximately ~3 nm diameter and a geometric deviation of ~0.2. Fe:Co ratios of 3:1, 4:1, and 5:1 were used in the synthesis, obtaining cobalt-substituted ferrites (Co_xFe_3-xO₄). Inductively coupled plasma mass spectroscopy (ICP-MS) verified the presence of cobalt in all samples. Fourier transform infrared (FTIR) spectra show bands at ~560 and ~400 cm^-1, confirming the metal-oxygen bond characteristic of ferrites. Despite the advantages posed by the reverse micelles, the method produces particles that are chemically bound to AOT. Bands observed at ~1725 cm^-1, ~1459 cm^-1, and ~1218 cm^-1 were attributed to AOT-particle bond. A lattice parameter value of a=8.388Å was obtained by X-ray for Co_0.61Fe_0.39O₄, which is near that of CoFe₂O₄(a=8.39Å). Magnetic measurements showed coercivities (H_c) higher than 8 kOe at 5K, whereas at 300K the particles showed superparamagnetic behavior. A rigorous analysis based on the Debye model for a magnetic dipole in an oscillating field was used to determine the anisotropy constant from AC susceptibility measurements. Assuming magnetic relaxation proceeds through the Néel mechanism, a relation between χ' and the temperature of the AC in-phase susceptibility curve peak was obtained. Using this relation, anisotropy constant values in the order of ~10⁶ kerg/cm³ were determined, whereas anisotropy constants in the order of ~10⁷ kerg/cm³ were calculated assuming Ωτ=1 at the temperature peak of the in-phase component of the susceptibility curve.