Spanish grape varieties that have been traditionally used to produce still wines were examined for their potential to make white and rosé sparkling wines. Sparkling wines manufactured from Vitis vinifera cv. Verdejo, Viura, Malvasía, Albarín, Godello, Garnacha, and Prieto varieties were examined for sensory attributes and for the evolution of monomeric and polymeric phenolics during different stages of winemaking and aging. Stabilization and clarification of the base wines significantly decreased the concentrations of anthocyanins and proanthocyanidins. During the initial months of aging on yeast lees, all types of polyphenols decreased, although some were released back into the wine during the final months. Garnacha rosé and Albarín white wines had high phenolic potential. Garnacha rosé sparkling wines had particularly high hydroxycinnamic acid concentrations, while Prieto Picudo rosé sparkling wines had the highest color intensity and anthocyanin concentrations. Among white sparkling wines, Albarín had the most catechin, proanthocyanidins, and, together with Viura, hydroxycinnamates. In sensory profiling, Prieto Picudo had more visual color intensity, red tones, olfactory intensity, freshness sensations, and foam quality than Garnacha wines. Albarín and Verdejo had more visual color and olfactory intensity than the other white wines, and Verdejo had better foam quality. Prieto Picudo, Albarín, and Verdejo were the most promising varieties for the production of high-quality sparkling wines.