QCD resummation predictions for the production of charged ( W ′ ) and neutral ( Z ′ ) heavy gauge bosons decaying leptonically are presented. The results of our resummation code at next-to-leading order and next-to-leading logarithmic (NLO+NLL) accuracy are compared to Monte Carlo predictions obtained with PYTHIA at leading order (LO) supplemented with parton showers (PS) and FEWZ at NLO and next-to-next-to-leading order (NNLO) for the p T -differential and total cross sections in the Sequential Standard Model (SSM) and general SU(2)×SU(2)×U(1) models. The LO+PS Monte Carlo and NNLO fixed-order predictions are shown to agree approximately with those at NLO+NLL at small and intermediate p T , respectively, and the importance of resummation for total cross sections is shown to increase with the gauge boson mass. The theoretical uncertainties are estimated by variations of the renormalisation/factorisation scales and of the parton densities, the former being significantly reduced by the resummation procedure. New limits at NLO+NLL on W ′ and Z ′ boson masses are obtained by reinterpreting the latest ATLAS and CMS results in general extensions of the Standard Model

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