The RCUK have published on their website a practical guide to help those planning their public engagement to include strong evaluation methods as part of their planning.
This guide is designed for those who lead projects intended to engage general audiences in science, social science, engineering and technology and the social, ethical and political issues that new research in these areas raises. It is intended to help project managers evaluate individual projects, regardless of their experience of evaluation. If you run, or oversee, lots of projects and report on them as a group, then
you should also look at the companion publication designed for programme managers.