We investigate whether national borders within Europe hinder the assortative matching of workers to firms in a high skilled labor market. We characterize worker productivity as the ability to contribute to physical output and define firm productivity as the capacity to transform physical output into revenues. We rank workers and firms according to their individual productivity estimates and study the ensuing rank correlation to gauge the degree of assortative matching within and across countries. We find strong evidence for positive assortative matching at the national level, and even more so at the international level. This suggests national borders do not prevent workers and firm from pursuing profitable complementarities in production.