The current study investigated the effectiveness of social robots in facilitating stress management interventions for university students by evaluating their physiological responses. We collected electroencephalogram (EEG) brain activity and Galvanic Skin Responses (GSRs) together with self-reported questionnaires from two groups of students who practiced a deep breathing exercise either with a social robot or a laptop. From GSR signals, we obtained the change in participants’ arousal level throughout the intervention, and from the EEG signals, we extracted the change in their emotional valence using the neurometric of Frontal Alpha Asymmetry (FAA). While subjective perceptions of stress and user experience did not differ significantly between the two groups, the physiological signals revealed differences in their emotional responses as evaluated by the arousal–valence model. The Laptop group tended to show a decrease in arousal level which, in some cases, was accompanied by negative valence indicative of boredom or lack of interest. On the other hand, the Robot group displayed two patterns; some demonstrated a decrease in arousal with positive valence indicative of calmness and relaxation, and others showed an increase in arousal together with positive valence interpreted as excitement. These findings provide interesting insights into the impact of social robots as mental well-being coaches on students’ emotions particularly in the presence of the novelty effect. Additionally, they provide evidence for the efficacy of physiological signals as an objective and reliable measure of user experience in HRI settings.