Anthropogenic sea level rise poses challenges to coastal areas worldwide, and robust projections are needed to assess mitigation options and guide adaptation measures. Here we present an approach that combines information about the equilibrium sea level response to global warming and last century's observed contribution from the individual components to constrain projections for this century. This "constrained extrapolation" overcomes limitations of earlier global semiempirical estimates because long-term changes in the partitioning of total sea level rise are accounted for. While applying semiempirical methodology, our method yields sea level projections that overlap with the process-based estimates of the Intergovernmental Panel on Climate Change. The method can thus lead to a better understanding of the gap between process-based and global semiempirical approaches.