Fluid film stiffness is a key design parameter for film-riding seals — a large positive film stiffness ensures stable seal operation with the seal faithfully tracking the rotor in the presence of varying inertial and friction loads. A hydrostatic supercritical CO2 (sCO2) film-riding seal relies on feed ports pressurized with sCO2 to generate film stiffness needed for reliable seal operation. The high-pressure supercritical CO2 expands to lower pressures through the seal bearing face, and during this expansion, undergoes large temperature changes along with a phase change to gaseous state and possibly liquid state. These large temperature changes and phase changes are important design considerations specific to sCO2 as the working fluid. From this perspective, film-stiffness test data with sCO2 as the working fluid is valuable for both understanding the physics as well as for validating the predictions of computational fluid dynamics (CFD) models of sCO2 expansion across a seal bearing face. In prior work, we described a non-rotating stiffness test rig for characterizing fluid film stiffness and presented air-based test data with the rig. In this paper, we present sCO2-based data obtained by connecting this previously described stiffness rig to a newly commissioned sCO2 flow loop (flow rate about 0.1 kg/s, pressures up to 16.5 MPa, temperatures up to 464 K). The test data presented in this paper include seal bearing pressures and fluid/metal temperatures for varying film thickness, seal bearing face tilt and inlet/supply pressures. The test data show significant temperature reduction as the supercritical flow expands across the seal bearing face. The measured bearing pressure was compared with the predictions of a 3D CFD model with real gas CO2 properties, with about 4% error between the measurements and the predictions. The sCO2-based test data in this work and the air-based test data from prior work are used to calculate fluid film stiffness over a range of film thicknesses. It is seen that the sCO2-based data and air-based data tend to collapse on a normalized stiffness curve, which is characteristic of the bearing geometry. Moreover, it is seen that the hydrostatic seal film stiffness generally scales with the supply pressure and can be adjusted to high stiffness values typically expected in hydrodynamic film-riding seals.