Transversal competences are now essential not only for employability but for the well-being of students, and thus for society as a whole. However, these competences are not commonly taught or researched as part of higher education degree programmes. This evidently leads to a gap between ideal teaching goals and what students actually learn in their undergraduate studies. To meet this need, a psychoeducational intervention was designed and implemented in an undergraduate programme in translation and interpreting within the framework of a teaching innovation project. The impact of this intervention was tested on transversal competences such as emotional intelligence and regulation, creativity, psychological distress, and cultural intelligence, among others. This parallel exploratory study compared the effectiveness of two mindfulness-based programmes. In both mindfulness-based training programmes, the preliminary results seemed to indicate an improvement in these transversal competences. Limitations of the study were the design, sample size, and the restrictions imposed by the COVID-19 pandemic. The results of our study led to recommendations for degree programme design as well as a platform for discussion and debate on the relationship between higher education, competence-based training, and social demands. The clinical trial was registered with www.clinicaltrials.gov (NCT04392869).