Agroindustrial waste can be valorized towards the obtaining of several products such as pigments, proteins, fibers, and polyphenolic compounds with antioxidant capacity. Orange peel waste is a promising source of polyphenolic compounds such as hesperidin. However, conventional extraction techniques present some environmental limitations such as high solvent consumption and high wastewater generation. Supercritical fluid extraction (SFE) has emerged as a green extraction technique due to the low use of solvent. The aim of this study was to maximize the hesperidin extraction based on theoretical predictions of the operating conditions from empirical thermodynamic models using SFE with carbon dioxide (CO2) as a solvent. The theoretical conditions were validated experimentally on a semi-pilot scale. The extracts were evaluated in terms of hesperidin content, total polyphenol content, and antioxidant capacity. Thermodynamic prediction of the operating conditions showed that the ethanol used as a co-solvent promotes hesperidin extraction. The optimum operating conditions were 25 °C, 80 bar, and a volumetric co-solvent concentration of 10%. The validation of the operating conditions resulted in a final hesperidin concentration of 11.5 ± 0.03 g/kg of orange peel waste. The experimental results were 30.26-times higher using 10% vol of ethanol than the extraction of hesperidin with pure ethanol as a co-solvent. The total polyphenol content and antioxidant capacity resulted in 831.92 ± 40.01 mg Galic acid/100 g orange peel waste, 15.41± 0.91 EC50/mL, and 5.31 ± 0.67 µMolTrox/100 g orange peel. Finally, the prediction of operating conditions from empirical thermodynamic models such as the Peng–Robinson equation of state with some modifications (Stryjek Vera) for solid–gas equilibrium solubility calculations, allows for maximizing the content of the polyphenolic compounds using SFE.