Drawbacks of current carbon dioxide capture methods include corrosivity, evaporative losses and fouling. Separating the capture solvent from infrastructure and effluent gases via microencapsulation provides possible solutions to these issues. Here we report carbon capture materials that may enable low-cost and energy-efficient capture of carbon dioxide from flue gas. Polymer microcapsules composed of liquid carbonate cores and highly permeable silicone shells are produced by microfluidic assembly. This motif couples the capacity and selectivity of liquid sorbents with high surface area to facilitate rapid and controlled carbon dioxide uptake and release over repeated cycles. While mass transport across the capsule shell is slightly lower relative to neat liquid sorbents, the surface area enhancement gained via encapsulation provides an order-of-magnitude increase in carbon dioxide absorption rates for a given sorbent mass. The microcapsules are stable under typical industrial operating conditions and may be used in supported packing and fluidized beds for large-scale carbon capture.