One of the challenges in the performance prediction of the supercritical CO2 (sc-CO2) compressor is the real gas behavior of the working fluid near the critical point. This study deals with the establishment of an approach that allows coping with this particularity by dressing compressor performance maps in adequate reduced coordinates (i.e., suitable dimensionless speed and flow parameters inputs and pressure ratio and enthalpy rise outputs), while using CFD for its validation. Two centrifugal compressor designs have been considered in this work. The first one corresponds to a 6 kW small scale component implemented in a test loop at Tokyo Institute of Technology. The second one corresponds to a 38 MW scale 1:1 design considered at an early stage of a project that investigates sc-CO2 cycle for a Small Modular Reactor application. Numerical results on the former have been successfully confronted with the experimental data to qualify the ability of CFD to provide a performance database. Results on the latter have revealed a significant decrease in the static temperature and pressure during flow acceleration along the leading edge of the impeller blades. In this line, the increased risk of vapor pockets appearance inside a sc-CO2 compressor has been highlighted and recommendations regarding the choice of the on-design inlet conditions and the compressor design have been given to overcome this concern. CFD results on the scale 1:1 compressor have then been used to evaluate the relevancy of some previous performance maps approaches for a sc-CO2 compressor application. These include the conventional approach for ideal gas and its derivation, as well as a reference approach from the literature that was previously applied to model a sc-CO2 test compressor. As the dimensionless parameters of these approaches are found to yield discrepancies on the compressor performance, a revised approach that incorporates real gas formulations into turbomachinery key similarity parameters has been finally proposed. In support, an extensive number of CFD case studies has been carried out at various compressor inlet conditions, providing numerical results for its qualification. Accordingly, the proposed approach has been found to succeed in consistently representing and accurately predicting the sc-CO2 compressor performance over a wide operating range.