The pisco industry generates significant environmental waste, particularly grape pomace, which is a rich source of phenolic compounds. Emerging extraction technologies offer promising alternatives for recovering these bioactive components. This study evaluated enzyme-assisted extraction (EAE) and pressurized liquid extraction (PLE) techniques using response surface methodology to optimize phenolic compound yield and antioxidant capacity. Specifically, a D-optimal design was applied for EAE, and a Box-Behnken design was applied for PLE. The optimal extraction conditions for EAE were 0.75 U/mL of tannase, 40 U/mL of cellulase, 20 °C, and 15 min. For PLE, the optimal parameters were 54% ethanol, 113 °C, and three extraction cycles. These conditions yielded 38.49 mg GAE g dw and 50.03 mg GAE g dw of total polyphenols and antioxidant capacities of 342.47 μmol TE g dw and 371.00 μmol TE g dw, respectively. The extracts obtained under optimal conditions were further characterized through chromatographic techniques to determine their phenolic profiles. Seven phenolic compounds were identified: gallic acid, catechin, epicatechin, 4-hydroxybenzoic acid, quercetin-3-rutinoside hydrate, quercetin-3-O-rhamnoside, and kaempferol. PLE extracts exhibited the highest concentration of these compounds. These findings demonstrate that recovering antioxidant-rich phenolic compounds from pisco grape pomace using innovative extraction methods is a viable strategy for obtaining functional ingredients and supporting sustainable industrial practices.