The magnetic remanence of silica microspheres with a low concentration of embedded cobalt ferrite nanoparticles is studied after demagnetization and remagnetization treatments. When the microspheres are dispersed in a liquid, alternating current (AC) magnetic susceptibility spectra reveal a constant characteristic frequency, corresponding to the rotational diffusion of the microparticles; this depends only on particle size and liquid viscosity, making the particles suitable as a rheological probe and indicating that interactions between the microspheres are weak. On the macroscopic scale, a sample with the dry microparticles is magnetically remanent after treatment in a saturating field, and after a demagnetization treatment, the remanence goes down to zero. The AC susceptibility of a liquid dispersion, however, characterizes the remanence on the scale of the individual microparticles, which does not become zero after demagnetization. The reason is that an individual microparticle contains only a relatively small number of magnetic units, so that even if they can be reoriented magnetically at random, the average vector sum of the nanoparticle dipoles is not negligible on the scale of the microparticle. In contrast, on the macroscopic scale, the demagnetization procedure randomizes the orientations of a macroscopic number of magnetic units, resulting in a remanent magnetization that is negligible compared to the saturation magnetization of the entire sample.