Vitis vinifera is the grape variety used in the production of wine and other products. In the wine production process, many of the vine’s by-products are wasted, namely seeds and stems. Given the proportion of wine production worldwide, the quantity of by-products is beginning to be an environmental problem, making it urgent to take measures for their use to obtain bioactive compounds with health benefits. The aim of this work was to study the antioxidant and antimicrobial activities of extracts from the seeds and stems of four Portuguese grape varieties: Touriga Franca, Touriga Nacional, Viosinho, and Tinta Roriz. Total phenolic (TPC) and total flavonoids (TFC) contents present in the different extracts were evaluated, as well as the antioxidant activity, by DPPH and FRAP methods. TPC and TFC values of the stem’s extracts are much higher than those of the seeds of the same grape variety in the same solvent. The antioxidant activity of aqueous and ethanolic stem extracts is higher than that obtained for the seeds, showing that antioxidant activity is related to the content of polyphenols. The antimicrobial activity of different stem and seed extracts was determined against yeasts and Gram-positive and Gram-negative bacteria, and the effect was determined based on the minimal inhibitory concentrations calculated (MIC). In general, the ethanol:water (1:1) extract of the seeds from the different varieties tested inhibited C. albicans ATCC10231 and C. krusei ATCC6258 growth even at 200 μg/mL, and the effect was fungicidal at 200 μg/mL. The same type of extract showed selective antimicrobial activity, inhibiting S. aureus ATCC29213 growth but having no effect against E. coli ATCC25922 even at 200 μg/mL. The effect against S. aureus was bactericidal (at 200 μg/mL) for Touriga Franca, Touriga Nacional, and Viosinho. Taking all these results into account, it can be concluded that the by-products of the grape varieties tested are important sources of bioactive products, particularly as antioxidants and antimicrobials.