  We consider favourable extensions of the standard model (SM) where the lepton
sector contains Majorana neutrinos with vanishing left-handed mass terms, thus
allowing for the see-saw mechanism to operate, and propose physical
on-mass-shell (OS) renormalization conditions for the lepton mixing matrices
that comply with ultraviolet finiteness, gauge-parameter independence, and
(pseudo)unitarity. A crucial feature is that the texture zero in the neutrino
mass matrix is preserved by renormalization, which is not automatically the
case for possible generalizations of existing renormalization prescriptions for
the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the SM. Our
renormalization prescription also applies to the special case of the SM and
leads to a physical OS definition of the renormalized CKM matrix.
