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 S=14  TeV with 3  ab−1 and S=27  TeV with 15  ab−1. A general technique for including next-to-leading order (NLO) QCD effects in effective field theory (EFT) fits to kinematic distributions is presented, and numerical results are given for 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 Hagiwara-Ishihara-Szalapski-Zeppenfeld 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 three-gauge-boson couplings.