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Trial and error remain the most common method to select the right solvent for the extraction of natural products, in particular when dealing with novel, poorly studied solvents such as deep eutectic solvents (DESs). This can lead to either a lengthy or a suboptimal selection of solvents. COSMO-RS, a quantum chemistrybased thermodynamic model, was applied in this work to screen the best DESs for the extraction of carnosic acid and carnosol, present in rosemary. Twenty-eight hydrogen bond acceptors (HBA) and fortynine hydrogen bond donors (HBD) were selected for the initial computational evaluation that revealed that hydrophobic DESs formed by ammonium chlorides as HBA, and the fatty acids, aromatic carboxylic acids, or alcohols as HBD to be the most suitable solvents for this extraction. Then, solid−liquid extractions were performed using these solvents to identify the best one and to optimize its composition. The ability of the solvents to obtain an extract rich in carnosic acid and carnosol was measured by the antioxidant activity of the extract, a mixture of 15 wt % of tetrapropylammonium chloride, 55 wt % of 1,2-propanediol, and 30 wt % of water being the solvent with the best performance. A response surface methodology was then carried out to optimize extraction conditions, in which antioxidant activity went up to 85 mg TE/g dw, that correspond to the extraction of 14.8 mg of carnosic acid and 18.9 mg of carnosol/g dw. Finally, the antioxidant activity of extracts obtained from a solvent without HBA was investigated. These aqueous mixtures of 1,2-propanediol showed a small loss in the performance. However, since the extraction process is simplified and this alcohol is biocompatible and allowed in formulations, the binary mixture seems to be a good, more sustainable alternative, to the ternary one.