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Capillary pressure (Pc) is one of the fundamental parameters in formation evaluation. Currently, three methods are routinely used for Pc measurement; i.e., mercury injection, centrifuge, and porous plate. All three methods require testing of fluid displacement at capillary equilibrium conditions, an often-challenging condition to obtain, especially in low-quality rock samples. In this study, the ability to derive Pc data was investigated using digital rock (DR) physics techniques. Two sister carbonate outcrop samples were prepared. The samples were initially analyzed using thin-section analysis technique. The Pc measurements were then performed using methods of porous plate and mercury injection capillary pressure (MICP). After that, the samples were sub-cored, mounted in a unique computed tomography (CT) cell, scanned with a high-resolution micro-CT device at a confining stress of 800 psig, and analyzed digitally with a scanning electron microscope for data interpretation. Comparing the physically measured to the digitally simulated data, matches of pore throat sizes in terms of trends and peaks were obtained, including entry pressure, which validated and confirmed the quality of the constructed DR models. Using the established digital models of the rock samples, the Pc behavior was simulated. The results showed trend and connate water saturation matches with the experimental measurements. The results of this study demonstrate that the digitally generated Pc data obtained using the unique micro-CT polyetheretherketone (PEEK) high-pressure cell match the experimental data, opening new ways of generating Pc data quickly and reliably. With the developed DR technologies, performing special core analysis tests much faster becomes a reality without concerns for test equilibrium conditions, while also providing informative insights into the pore structure of the rock samples.