$W$ bosons decay into an electron and electron-neutrino
or into a muon and muon-neutrino. The $W$ lifetime is about $3 \cdot 10^{-25}\ \rm s$. That means the decay occurs close to the collision point, not in a detector.

The energy of the resulting electron or muon can be measured
quite accurately, but for the neutrino the energy
must be inferred (with a low accuracy).

How can one arrive at a precision like $80.385 \pm 0.015\ \rm GeV$
for the $W$ boson rest energy, as it is quoted in the literature?

(similar arguments apply to the $Z$)