About half of annual marine carbon burial takes place in shallow water ecosystems where geomorphic and ecological stability is driven by interactions between the flow of water, vegetation growth and sediment transport(1). Although the sensitivity of terrestrial and deep marine carbon pools to climate change has been studied for decades, there is little understanding of how coastal carbon accumulation rates will change and potentially feed back on climate(2,3). Here we develop a numerical model of salt marsh evolution, informed by recent measurements of productivity and decomposition, and demonstrate that competition between mineral sediment deposition and organic-matter accumulation determines the net impact of climate change on carbon accumulation in intertidal wetlands. We find that the direct impact of warming on soil carbon accumulation rates is more subtle than the impact of warming-driven sea level rise, although the impact of warming increases with increasing rates of sea level rise. Our simulations suggest that the net impact of climate change will be to increase carbon burial rates in the first half of the twenty-first century, but that carbon-climate feedbacks are likely to diminish over time.