  We study the impact of anomalous gauge boson and fermion couplings on the
production of $W^+W^-$ pairs at potential future LHC upgrades and estimate the
sensitivity at $\sqrt{S}=14$ TeV with $3~ab^{-1}$ and $\sqrt{S}=27$ TeV with
$15~ab^{-1}$. A general technique for including NLO QCD effects in effective
field theory (EFT) fits to kinematic distributions is presented, and numerical
results are given for $\sqrt{S}=13$ TeV $W^+W^-$ production. Our method allows
fits to anomalous couplings at NLO accuracy in any EFT basis and has been
implemented in a publicly available version of the POWHEG-BOX. Analytic
expressions for the $K$-factors relevant for $13$ TeV total cross sections are
given for the HISZ and Warsaw EFT bases and differential $K$-factors can be
obtained using the supplemental material. Our study demonstrates the necessity
of including anomalous $Z$- fermion couplings in the extraction of limits on
anomalous 3-gauge-boson couplings.
