To mitigate the model dependencies of searches for new narrow resonances at the Large Hadron Collider (LHC), semi-supervised Neural Networks (NNs) can be used. Unlike fully supervised classifiers these models introduce an additional look-elsewhere effect in the process of optimising thresholds on the response distribution. We perform a frequentist study to quantify this effect, in the form of a trials factor. As an example, we consider simulated Zγ data to perform narrow resonance searches using semi-supervised NN classifiers. The results from this analysis provide substantiation that the look-elsewhere effect induced by the semi-supervised NN is under control.