Responsible innovation has emerged as a field of research dedicated to introduce sensitivity to societal values in innovation processes. However, much of the academic literature on RI deals with single technologies instead of technological systems and is future-orientated without explicitly using specialised knowledge of past developments. In this paper, we present a problem-focused approach to RI that aims to support researchers and stakeholders in developing potential solutions from a perspective of systemic awareness and historical sensitivity. We then describe the application of this approach in an 18 months long interdisciplinary research project on plastics. We show that the approach has generated new and unexpected research projects, formed new inter- and transdisciplinary collaborations, and has impacted some participants’ understanding of the systems in which their work is embedded. We conclude that with appropriate willingness to engage by individual researchers, our approach is able to, firstly, influence highly experienced researchers to engage more responsibly with their work, and secondly, to make research projects responsive by including societal concerns and their historical emergence from the start.