Literature in Human–Computer and Human–Robot Interaction shows how empathic agents enhance user experience, in healthcare, education, and other contexts. This study provides an analysis of being moved, an emotion closely connected to empathy, exploring its potential in enhancing artificial agents’ empathic capabilities. Starting from a socio-cognitive model, a survey study involving 128 participants identified the “mental ingredients” of this emotion, the conditions that trigger it, and its biological functions. Four types of being moved are distinguished: personal goal, empathic response, good world contemplation, and aesthetic appreciation. It is also highlighted how this emotion often blends positive and negative feelings and is closely tied to empathy. As for the future development of this research, further work is proposed to exploit the Large Language Model architecture in training an empathic chatbot to detect when a user is moved, possibly to express this emotion itself, thus better conveying empathy and fostering deeper emotional connections with users.