The assessment process in higher education considers four aspects: assessment agents, procedure, content, and scoring. In this study, we delve into the who. We analyze the role of transversal competence assessment agents in the framework of professional internships in university master's degree programs, comparing the suitability of their assessment based on their degree of experience in each master's program. Four university master's degree programs, in the field of human and social sciences, were analyzed. To ensure the degree of expert competence among the participating judges, the K coefficient was used. Two expert and two nonexpert judges independently assessed the critical incidents narrated by the students and inquired about the competences described in the curricula. The reliability index between the assessments from expert and nonexpert judges was analyzed. The results show greater reliability among the assessments of expert judges compared to nonexperts. As a result, we conclude the importance of basing the selection of assessors on objective expert competence and not on criteria more linked to academic management. It is also necessary to include the critical incident method as a systematic information collection system to explicitly assess transversal competences.