Distilled white grape pomace (Vitis vinifera var. Garnacha) was subjected to extraction by using two different methods: (1) solid–liquid extraction (SLE) employing 96% ethanol and water and (2) supercritical extraction (SFE) by running carbon dioxide coupled with ethanol as a modifier. Higher phenolic concentrations of extracts were attained by SFE (∼400 ppm), doubling those obtained by SLE. In the latter, increasing values of both temperature (from 25 to 50 °C) and contact time (from 30 to 90 min) and lower solvent-to-solid ratios (from 5:1 to 1:1) resulted in an enhancement of extraction efficiency. In SFE, the addition of the modifier (8%) was also found to favour the release of phenolic compounds. Antiradical activity values—evaluated by the ability to scavenge DPPH radicals—were, as general, also higher for SFE extracts, although maximum values reached at were similar (73% inhibition versus 68%). Chromatographic profiles confirmed the diverse nature of phenolic species occurring in extracts obtained from both extraction methods. Extracts from SLE contained more proanthocyanidins, whereas SFE ones contained basically gallic acid, catechin and epicatechin. Protection against oil oxidation assayed with two samples confirmed these results.