The presented research claims that cross-border tandem projects can be exploited in Higher Education Institutions (HEIs) as a powerful tool to develop foreign language proficiency, 21st century skills, and professional expertise. An international tandem project was conducted between two HEIs — the Czech ŠKODA AUTO University and the Austrian University of Applied Sciences Upper Austria. Each student pair undertook a research project on a mutually agreed topic in English and presented it through an abstract, academic poster, and video presentation. The tandem project cooperation is discussed from the students’ perspective using a thematic analysis of critical incidents shared through focus groups, interviews, and student written accounts. Attention was paid to how students handled time management, problem solving, responsibility sharing, how they saw their learning and personal development, as well as how their teachers managed the project to propose a tandem-project pedagogical approach for educators. It was found that, despite initial uncertainties and problems, the experience enhanced the students’ English language proficiency, expanded their intercultural knowledge and expertise, developed 21st century skills, and promoted international networking.