The scientific community of educators has been more and more interested in Tinkering as an informal method to engage students with STEM subjects. Recent research has highlighted that Tinkering could be adopted not only to develop students’ scientific knowledge but also to support thinking processes such as Critical Thinking and Creative Problem Solving. Despite these assumptions, there is still a lack of research concerning the impact of Tinkering on the development of the 21st Century skills. That is why the Centre investigated the impact of Tinkering activities on Critical and Creative thinking skills enhancement in museum educators and teachers involved in STEM education. The Centre conducted a pilot study with 30 participants at Città della Scienza science centre (Naples), where museum educators and STEM teachers participated in a two-day workshop on collaborative Tinkering activities. During the workshop, participants were required to take two kinds of pre and post-tests with the aim of assessing Critical and Creative thinking skills development. On the one hand, in the Creative Thinking post-test participants showed significant improvement. On the other hand, despite there were no statistical differences concerning Critical Thinking assessment, a slight improvement in the post-test could be quantified. Follow up research is required, where it will be necessary to expand the sample of the study and use different measures for Critical and Creative Thinking assessment.