In this examination, two glycerol-based deep eutectic solvents (DESs) were tested for their efficiency in the recovery of antioxidant polyphenols and anthocyanin pigments from red grape pomace (RGP). The two DESs synthesized had sodium acetate and sodium benzoate as hydrogen bond acceptors, to test the role of the hydrogen bond acceptor polarity on the extraction performance. Furthermore, the process was enhanced by an ultrasonication pretreatment stage. After initial testing with respect to water content, ultrasonication power and liquid-to-solid ratio, the DES composed of glycerol and sodium benzoate (GL-SBz) was shown to be significantly more efficient than the one made of glycerol and sodium acetate (GL-SAc). Further optimization of the extraction with regard to time and temperature demonstrated GL-SBz to be a highly effective solvent for the production of RGP extracts rich in polyphenols including gallic acid, catechin and quercetin, and pigments including malvidin 3-O-glucoside p-coumarate and malvidin 3-O-glucoside. The extracts produced also had significantly higher antiradical activity and reducing power compared to those generated with aqueous ethanol or water. From this study, evidence emerged regarding the role of the hydrogen bond acceptor nature in the extraction efficiency of polyphenols. The process developed is proposed as a green, high-performing methodology for the production of RGP extracts with enhanced polyphenolic content and antioxidant activity.