A methodology is presented for the objective and transparent screening of hydrocarbon reservoirs for underground hydrogen storage (UHS), with subsequent testing on a large confidential dataset provided by the energy company Eni. The procedure uses the Analytic Hierarchy Process and the Delphi technique to gather expert opinions and weight 27 screening parameters in terms of: health, safety, and environment; geotechnical performance; and economic performance. A set of scores is produced that characterizes each site in terms of these three categories, as well as a comprehensive site ranking based on their overall suitability for UHS. The results highlight the importance of geotechnical parameters, while the characterization of faults and hydrocarbon type, the onshore or offshore location, the number of wells, and the reservoir architecture yielded the highest individual weights. Potential scores are also estimated for sites with incomplete datasets. Two blind tests evaluated the method's effectiveness against preexisting industrial assessments.