PurposeThis paper addresses the relevance of job search methods and strategies in determining vertical mismatch and the risk of underusing skills or knowledge in first jobs amongst graduates from bachelor's and master's programmes in Spain. Support from universities (via internships and career services) is compared to support from public institutions and informal strategies.Design/methodology/approachThe authors use the 2019 University Graduate Job Placement Survey. The dependent variables are estimated with a bivariate probit model with sample selection on a subsample of graduates who were not working at graduation.FindingsInternships and university career employment offices significantly improve the quality of first job matches. Job banks and public examinations also contribute to finding well-matched first positions, while for public employment services, results are mixed. When the job search is not supported by institutions, graduates generally do worse finding their first jobs, particularly when temporary employment agencies are involved. There are also large differences in mismatch risks across fields of study.Practical implicationsIf more graduates found their first jobs through internships and university job placement services, educational mismatch rates would decrease substantially. Further collaboration between universities and employers for the provision of high-quality internships may foster their conversion into regular, well-matched jobs. Industrial policies addressed to knowledge-based economic activities would enhance the creation of highly skilled positions. Further orientation towards STEM degrees is required to improve imbalances between supply and demand for graduate labour in Spain.Originality/valueEvidence about education mismatch among master's degree graduates is very scarce. This paper compares them to bachelor's degree graduates. It addresses two complementary types of education mismatch and takes into account potential self-selection into post-graduation job search.