Different white winemaking byproducts (pomace, skins, seeds, and stems) were compared as natural sources of phenolic compounds having biological and sensory properties of enological interest. Antioxidant and copigmentation effects of these byproducts were studied in a wine-like model solution. RRLC-DAD was used to establish differences in the phenolic composition, and the ABTS method was used to compare the antioxidant activities. Spectrophotometric and colorimetric analyses were performed to assess the magnitude of copigmentation and the changes induced in the color expression of red wine anthocyanins. Antioxidant and copigmentation properties significantly varied depending on the type of byproduct, which was related to their qualitative and quantitative phenolic composition. Seeds and pomace showed the highest antioxidant potential, whereas skins and pomace led to the strongest and visually perceptible color effects on red wine anthocyanins by multiple copigmentation (darker, more saturated, and vivid bluish colors). Results open the possibility of technological applications for the wine industry based on reusing winemaking byproducts to improve the biological value and color characteristics of red wines.