There are large amounts of data that are collected, processed and exchanged in projects and they form the basis of innovation and fact-finding activities that are at the core of project activities. Nevertheless, such data can be irresponsibly used, managed and governed during its lifecycle, starting from creation all the way to its use. Given the importance of data and the risk of being misused, it is important to understand how responsibilities for data management can or should be designed in projects. This paper showcases how the concept of Responsible Research and Innovation (RRI) can be implemented in projects to mitigate irresponsible data management and use. The paper draws on the practices undertaken in two EU funded research projects to help practitioners find ways of dealing with data management related issues.