Abstract: Non-unitarity of the neutrino mixing matrix is expected in many scenarios with physics beyond the Standard Model. Motivated by the search for deviations from unitary, we study two neutrino counting observables: the neutrino-antineutrino gamma process and the invisible Z boson decay into neutrinos. We report on new constraints for non-unitarity coming from the first of these observables. We study the potential constraints that future collider experiments will give from the invisible decay of the Z boson, that will be measured with improved precision.