Finding robust explanations of behaviours in Alife and related fields is made difficult by the lack of any formalised definition of robustness. A concerted effort to develop a framework which allows for robust explanations of those behaviours to be developed is needed, as well as a discussion of what constitutes a potentially useful definition for behavioural robustness. To this end, we describe two senses of robustness: robustness in systems; and robustness in explanation. We then propose a framework for developing robust explanations using linked sets of models, and describe a programme of research incorporating both robotics and chemical experiments which is designed to investigate robustness in systems.