The outbreak of the global pandemic derived from COVID-19 in early 2020 has represented a huge loss of social contact for most young people. The extent of these effects is still unknown, so it is necessary to ask what the effect of this new, unforeseen, and prolonged situation on the management of emotional intelligence in university students is. This study aims to compare the academic performance, test anxiety (before and during the online exams), and emotional intelligence of 91 students in a university Master’s degree program after the outbreak of the COVID-19 pandemic. The emotional intelligence was measured by the TMMS-24, the academic performance was compiled in common subjects, and test anxiety was measured by self-assessment just after finishing each online exam. The comparisons between the variables were made through means difference contrasts using Mann–Whitney U, Kruskal–Wallis, and One-way ANOVA and Spearman’s rank correlation coefficient as a non-parametric test for correlational analysis. The results show that the COVID-19 pandemic has not modified how these three variables are related, so it can be concluded that the prolonged social isolation suffered by young people has not had negative repercussions on their emotional intelligence, anxiety before exams, and academic performance.