The integration of AI-driven solutions in healthcare is revolutionizing various domains, spanning from pathology and radiology to neonatal intensive care and homecare. This transformative shift not only alters the workflows of healthcare professionals but also reshapes the experience of patients and informal caretakers. Amidst this development, an often-overlooked facet is the impact on emotional relationships among the diverse stakeholders in healthcare. This paper aims to cover this gap by combining insights from the theory of technological mediation and philosophy of emotions: by using the introduction of Artificial Intelligence (AI) in the healthcare field as an example, we showcase how the technological mediation approach has so far overlooked the role of moral emotions in the analysis of how technologies mediate moral life. By building on the concept of emotional attunement, we present an understanding of emotions as practices, where technologies act as mediators of the way in which subjects emotionally attune to each other. We subsequently argue that this mediation is revealed the moment technologies come to create frictions in the attuned emotional practice. These perturbations of emotional attunements are what we call ‘emotional glitches’. It is through glitches that moral and emotional mediation of technologies is revealed, thereby also highlighting normative aspects. We argue that studying moral technological mediation through emotional glitches can provide insightful observations on how these technologies should be developed and deployed.