Carbonate reservoirs represent a possible geological storage option for carbon dioxide from anthropogenic sources. We conducted capillary trapping experiments on different carbonate rocks to assess their suitability for storage. We measured the trapped non-wetting phase saturation as a function of the initial non-wetting phase saturation and porosity. We used refined oil – with a density similar to that of supercritical CO2 – as the non-wetting phase and brine as the wetting phase. The experiments were performed at ambient temperature and slightly elevated pressures. Saturations were determined by mass and volume balance. We found that the trapped non-wetting phase saturation rises approximately linearly with initial saturation. The porosity was shown to have a significant effect on both initial saturation and residual saturation. The influence of effective stress was also investigated. It was shown that carbonates have significantly different stress behavior compared to sandstones. As the pressure of the non-wetting phase increases during primary drainage, the initial oil saturation increases to a maximum value and then decreases, as the fluid pressure affects the pore structure of the rock.