We present predictions for the associated production of a Higgs boson at NLO+PS accuracy, including the effect of anomalous interactions between the Higgs and gauge bosons. We present our results in different frameworks, one in which the interaction vertex between the Higgs boson and Standard Model W and Z bosons is parameterized in terms of general Lorentz structures, and one in which Electroweak symmetry breaking is manifestly linear and the resulting operators arise through a six-dimensional

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... effective field theory framework. We present analytic calculations of the Standard Model and Beyond the Standard Model contributions, and discuss the phenomenological impact of the higher order pieces. Our results are implemented in the NLO Monte Carlo program MCFM, and interfaced to shower Monte Carlos through the Powheg box framework.