The magnetic properties of bimagnetic core/shell nanoparticles consisting of an antiferromagnetic MnO core and a ferrimagnetic passivation shell have been investigated. It is found that the phase of the passivation shell (gamma-Mn2O3 or Mn3O4) depends on the size of the nanoparticles. Structural and magnetic characterizations concur that while the smallest nanoparticles have a predominantly gamma-Mn2O3 shell, larger ones have increasing amounts of Mn3O4. A considerable enhancement of the Neel temperature, T-N, and the magnetic anisotropy of the MnO core for decreasing core sizes has been observed. The size reduction also leads to other phenomena such as persistent magnetic moment in MnO up to high temperatures and an unusual temperature behavior of the magnetic domains.