We report a detailed experimental study of maghemite nanoparticles, with sizes ranging from 1.6 to 6 nm, synthesized inside a biological mould of apoferritin. The structural characterization of the inorganic cores, using TEM and x-ray diffraction, reveals a low degree of crystalline order, possibly arising from the nucleation and growth of multiple domains inside each molecule. We have also investigated the molecular structure by means of atomic force microscopy in liquid. We find that the synthesis of nanoparticles inside apoferritin leads to a small, but measurable, decrease in the external diameter of the protein, probably associated with conformational changes. The magnetic response of the maghemite cores has been studied by a combination of techniques, including ac susceptibility, dc magnetization and Mössbauer spectroscopy. From the equilibrium magnetic response, we have determined the distribution of magnetic moments per molecule. The results show highly reduced magnetic moments. This effect cannot be ascribed solely to the canting of spins located at the particle surface but, instead, it suggests that magnetoferritin cores have a highly disordered magnetic structure in which the contributions of different domains compensate each other. Finally, we have also determined, for each sample, the distribution of the activation energies required for the magnetization reversal and, from this, the size-dependent magnetic anisotropy constant K. We find that K is enormously enhanced with respect to the maghemite bulk value and that it increases with decreasing size. The Mössbauer spectra suggest that low-symmetry atomic sites, probably located at the particle surface and at the interfaces between different crystalline domains, are the likely source of the enhanced magnetic anisotropy.