Face recognition and classification systems are typically designed to identify and classify images of people who have participated previously in the training phase of a Deep Learning system, referred to as known identities. This corresponds to a closed-set scenario, which commonly employs a SoftMax layer as the final layer of a Convolutional Neural Network. However, this SoftMax layer encounters significant difficulties in open-set scenarios, where it is often unable to differentiate between known and unknown identities during the testing phase. Consequently, OpenMax emerges as a solution for open-set scenarios. Considering the context, this paper presents an optimization of the OpenMax parameters for open-set face recognition scenarios. The results indicate that the tail size and the number of top classes to revise should be set to 5 and 2, respectively. In contrast, the threshold and the distance measure are less critical parameters that can take different values while obtaining similar results. Furthermore, the accuracy of the open-set face recognition scenario demonstrated in previous studies has been enhanced through the optimization of the OpenMax parameters.