  The proposed electron-proton collider experiments LHeC and FCC-eh at CERN are
the highest resolution microscopes that can be realised in the present century
and they would represent a really unique research facility. We exploit
simulated neutral-current and charged-current deep-inelastic scattering data of
the LHeC and the FCC-eh and examine their sensitivity for precision physics in
the Electroweak sector of the Standard Model (SM), like the effective weak
mixing angle $\sin^2\theta_{\textrm{W},\ell}^\textrm{eff}$, or the light-quark
weak-neutral-current couplings. Unique measurements are further feasible at
high precision for the running of the weak mixing angle, as well as for
electroweak effects in charged current interactions. The sensitivity to beyond
SM effects is studied using the generic $S$, $T$ and $U$ parameterization. The
report summarizes previous studies about the LHeC and presents new prospects
for the FCC-eh.
