This paper focuses on the design of a serious game for the teaching and assessment of generic competences, placing particular emphasis on the competences assessment aspect. Taking into account important aspects of competence assessment such as context, feedback and transparency, among other aspects, and using the University of Deusto's Generic Competences Assessment Model based on the defining of levels, indicators and descriptors as a reference point, a serious game has been designed for the development and evaluation of two Generic Competences: Problem Solving and Entrepreneurship, aimed at final-year undergraduate and first-year postgraduate students. The design process shows that having a Competence Assessment Model based on levels, indicators and descriptors is of great help in defining the game's scenarios and learning and assessment activities. Serious games can also be excellent resources to help in the development and assessment of generic competences, but not as a unique tool, since the concept of competence in itself is highly complex (integrating knowledge, skills, attitudes and values) and some elements might require other methods and techniques for its development. It also reveals the difficulties of evaluating competences in general and through serious games in particular.