The problem of abstaining from making uncertain predictions has received rising interest in the last few years. However, even if introducing a reject option for a machine learning model in a supervised scenario has already been addressed in many works in literature, it seems to be a completely unexplored field for anomaly detection, where few or no labels are available and making a misclassification can be very expensive for a company. In this work, we introduced a novel technique for anomaly detectors to abstain from making uncertain predictions, introducing a reject option for both unsupervised and semi-supervised scenarios. The novel framework, being based on a dependent rejector making use of the model confidence, is exploitable without regard to the anomaly detector chosen.