Positron lifetime and coincidence Doppler broadening measurements on ZrO2+3 mol.% RE2O3 (RE = Eu, Gd, Lu) nanopowders and ceramics obtained by sintering these nanopowders are reported. The initial nanopowders were prepared by a co-precipitation technique and exhibited a mean particle size of ≈ 15 nm. The nanopowders were calcined and pressure-compacted. All compacted nanopowders exhibited the prevailing tetragonal phase with at most 15% of the monoclinic admixture. Positrons in compacted nanopowders were found to annihilate almost exclusively at grain boundaries: (i) vacancy-like misfit defects along grain boundaries and (ii) larger defects situated at intersections of grain boundaries (triple points). In nanopowders, a small portion of positrons formed positronium in pores between crystallites. Sintering of nanopowders at 1500 °C caused a substantial grain growth and formation of ceramics. Sintering-induced grain growth led to a disappearance of the triple points and pores. The ceramics containing Eu and Gd dopants consist of mixture of the monoclinic and the tetragonal phase, while the ceramics with Lu dopant exhibits almost exclusively the tetragonal phase.