  We point out that right-handed neutrinos can resolve the tension between the
latest CDF II measurement of the $W$-boson mass, $M_W$, and the standard model.
Integrating out the new states yields a single $d=6$ operator, which induces a
deviation from unitarity in the PMNS matrix. This alters the extraction of the
Fermi constant from muon decay and increases the prediction for $M_W$, in line
with the CDF II result. Non-unitarity of the PMNS matrix would also affect
beta, meson, and tau decays. We find that the CDF II value for $M_W$ can be
explained without conflicting with lepton flavour universality constraints or
the invisible decay width of the $Z$. However, the so-called Cabibbo angle
anomaly is worsened if right-handed neutrinos are the origin of the $d=6$
operator. The situation improves if the operator coefficient is left
unconstrained, implying additional sources of new physics, but a common
explanation of both anomalies is in tension with universality bounds.
