The conventional approach to sustainability is being extended through approaches such as the psychology of sustainability and sustainable development. Under such approaches, the analysis of sustainability also involves understanding improvements in people’s quality of life in environments such as education and learning. Based on this theoretical approach, this study explored the relationships between anxiety, emotional intelligence, and mechanisms for coping with stressful situations. The mediating role of emotional intelligence in the relationship between anxiety and coping mechanisms was also assessed. The anxiety, emotional intelligence, and coping variables were measured using standardized tests administered to students. This cross-sectional study was based on self-reports by health students at universities in Valencia (Spain). The study conformed to the ethical standards established by the Declaration of Helsinki. In total, 434 students participated in the study. The students were aged between 17 and 54 years (M = 21; SD = 0.320). From the perspective of the psychology of sustainability, the results indicate that avoidance coping strategies are positively related to anxiety and are negatively related to emotional intelligence. However, the results also show that approach coping strategies are positively related to emotional intelligence. In addition, the analysis shows the mediating role of emotional intelligence in the relationship between anxiety and coping. This study shows the need to encourage the sustainable development of emotional intelligence among health professionals and to consider this sustainable development when designing education programs for health-related fields.