Assumptions of a static landscape inspire predictions that about half of the world's coastal wetlands will submerge during this century in response to sea-level acceleration. In contrast, we use simulations from five numerical models to quantify the conditions under which ecogeomorphic feedbacks allow coastal wetlands to adapt to projected changes in sea level. In contrast to previous sea-level assessments, we find that non-linear feedbacks among inundation, plant growth, organic matter accretion, and sediment deposition, allow marshes to survive conservative projections of sea-level rise where suspended sediment concentrations are greater than ~20 mg/L. Under scenarios of more rapid sea-level rise (e.g., those that include ice sheet melting), marshes will likely submerge near the end of the 21st century. Our results emphasize that in areas of rapid geomorphic change, predicting the response of ecosystems to climate change requires consideration of the ability of biological processes to modify their physical environment.