Grape pomace is the main by-product obtained from wine production that is still enriched in bioactive compounds. Within a framework of waste/by-product reuse through a sustainable approach, various green methods were utilized in this work to recover anthocyanins from the pomace resulting from “Sangiovese” grape vinification. Ultrasound- and Microwave-Assisted Extractions (UAE and MAE) were coupled with the use of green solvents, such as acidified water, an ethanol/water mixture, and Natural Deep Eutectic Solvents (NaDES), and their efficacy was compared with that of a conventional method based on a methanol/acidified water mixture. The Total Anthocyanin Index ranged from 36.9 to 75.2 mg/g DW for UAE, and from 54.4 to 99.6 mg/g DW for MAE, while resulting in 47.1 mg/g DW for conventional extraction. A Design of Experiments (DoE) approach was applied to MAE, the most efficient technique. Temperature, time, and the solid-to-liquid ratio were set as X variables, while malvidin-3-O-glucoside content and antioxidant activity were used as response variables, measured by High-Performance Liquid Chromatography with Diode Array Detection (HPLC-DAD) and 2,2-Diphenyl-1-picrylhydrazyl (DPPH) assay, respectively. The correlation between temperature and time and the antioxidant activity of the extract was positive, while it was found to be negative when considering malvidin-3-O-glucoside concentration as a response variable. Thus, the optimal conditions in temperature, time and solid-to-liquid ratio were different depending on the chosen variable. The results underline the importance of selecting an accurate response when using the response surface methodology approach.