We present studies of single-phase multiferroic materials in nanoparticle or nanoplate form, where size effects modify the long range magnetic structure and hence influence the magnetic properties. Size effects as isolated here, are of particular relevance to understand the interplay between magnetic and ferroelectric properties in heterogeneous, multi-phase multiferroic structures. Bulk multiferroic BiMnO3 shows ferromagnetic ordering below 105 K, but few characterization attempts have been performed on nanoscaled material. We have synthesized BiMnO3 nanoplates and characterized the structure, composition, morphology and magnetic properties. Ferromagnetic behavior is not observed in the nanoplates, in contrast to the bulk, indicative of finite size effects. We have also synthesized BiFeO3 nanoparticles (characterized by XRD, EDS and magnetometry), which exhibit ferromagnetism with spin-glass-like behavior, as a result of reduced dimensionality. Bulk perovskite BiFeO3 instead shows antiferromagnetism. The difference in magnetic behavior for nanoparticles compared to bulk behavior, is, in both cases, attributable to finite-size effects.