We show how to deal with uncertainties on the Reference Model predictions in a signal-model-independent new physics search strategy based on artificial neural networks. Our approach builds directly on the Maximum Likelihood ratio treatment of uncertainties as nuisance parameters for hypothesis testing that is routinely employed in high-energy physics. After presenting the conceptual foundations of the method, we show its applicability in a multivariate setup by studying the impact of two typical sources of experimental uncertainties in two-body final states at the LHC.