As partners in a European project for responsible research and innovation (RRI) in synthetic biology, we organized a collaborative and interactive process of real-time technology assessment. This process consisted of two related activities complementing each other as different modes of future making, one focussing on technological options, the other on societal objectives. For the first type of activity, we established a three-year collaboration with the annual international Genetically Engineered Machines competition, stimulating student teams to consider the wider societal ramifications of future options for innovation in synthetic biology. As a follow-up activity in this process of real-time and anticipatory technology assessment, we involved a variety of societal stakeholders and researchers in synthetic biology in workshop dialogues focusing on antibiotic resistance and renewable energy as societal challenges. We invited the participants to critically consider the nature of these challenges and related value-laden issues of concern, and to define in this context opportunities and needs for innovation in synthetic biology. We see both approaches as vital in fulfilling the ambitions of responsible research and innovation. In terms of the governance of innovation, we emphasize the need for a proper toolbox and a co-creation infrastructure as crucial requirements for inclusive, reflexive and responsive practices of future making.