The development of 64Cu-based immuno-PET radiotracers requires the use of copper-specific bifunctional chelators (BFCs) that contain functional groups allowing both convenient bioconjugation and stable copper complexes to limit in vivo bioreduction, transmetallation and/or transchelation. The excellent in vivo kinetic inertness of the pentaazamacrocyclic 64CuCu-15-5 complex prompted us to investigate its potential for the 64Cu-labelling of monoclonal antibodies (mAbs), compared with the well-known NODAGA and DOTA chelators. To this end, three NODAGA, DOTA and 15-5-derived BFCs, containing a pendant azadibenzocyclooctyne moiety, were synthesised and a robust methodology was determined to form covalent bonds between them and azide-functionalised trastuzumab, an anti-HER2 mAb, using strain-promoted azide-alkyne cycloaddition. Unlike the DOTA derivative, the NODAGA- and 15-5-mAb conjugates were radiolabelled with 64Cu, obtaining excellent radiochemical yields, under mild conditions. Although all the radioimmunoconjugates showed excellent stability in PBS or mouse serum, 64CuCu-15-5- and 64CuCu-NODAGA-trastuzumab presented higher resistance to transchelation when challenged by EDTA. Finally, the immunoreactive fraction of the radioimmunoconjugates (88–94%) was determined in HER-2 positive BT474 human breast cancer cells, confirming that the bioconjugation and radiolabelling processes implemented had no significant impact on antigen recognition.