Achieving climate policy targets will require large-scale deployment of low-carbon energy technologies, including nuclear power. The small modular reactor (SMR) is viewed as a possible solution to the problems of energy security as well as climate change. In this paper, we use an integrated assessment model (IAM) to investigate the evolution of a global energy portfolio with SMRs under a stringent climate policy. Technology selection in the model is based on costs; we use results from previous expert elicitation studies of SMR costs. We find that the costs of achieving a 2oC target are lower with SMRs than without. The costs are higher when large reactors do not compete for market share compared to a world in which they can compete freely. When both SMRs and large reactors compete for market share, reduction in mitigation cost is achieved only under advanced assumptions about SMR technology costs and future cost improvements. While the availability of SMRs could lower mitigation costs by a moderate amount, actual realization of these benefits would depend on the rapid up-scaling of SMRs in the near term. Such rapid deployment could be limited by several social, institutional and behavioral obstacles.