Simulation games are increasingly popular tools for opening up future imaginaries, especially in the arena of sustainability policy-making and decision support. However, there is a lack of understanding regarding the potential power of games in anticipatory governance. We argue that the utility of simulation games in support of anticipatory climate governance can be greatly increased when game processes are consciously designed to impact present day planning and action. At the same time, game designers with the intention to support or intervene in governance and policy-making inevitably enter political arenas and bear responsibility for understanding and managing their influence at the science-policy interface. We present two case studies: a game simulating a sustainable food policy council with food system actors in Kyoto, Japan, and a game focused on the exploration and imagination of the global impacts of climate tipping points aimed at participants of the global climate negotiation community. Each case study represents a specific logic for translating game play into real-world impacts at different governance scales with distinct political implications. Based on these two case studies, we develop principles for the design and evaluation of simulation games that seek to impact anticipatory climate governance, based on five lenses: (1) purpose and positionality; (2) conceptions of the future and imaginaries; (3) beneficiaries, key stakeholders and participants; (4) the politics of game features and design; and (5) evaluation.