The present work aims to study the possibilities of developing silver nanoparticles using natural extracts of grape pomace wastes originating from the native variety of Fetească Neagră 6 Șt. This study focused on investigating the influence of grape pomace extract obtained by two different extraction methods (classical temperature extraction and microwave-assisted extraction) in the phytosynthesis process of metal nanoparticles. The total phenolic content of the extracts was assessed using the spectrophotometric method with the Folin–Ciocâlteu reagent, while the identification and quantification of specific components were conducted through high-performance liquid chromatography with a diode array detector (HPLC-DAD). The obtained nanoparticles were characterized by UV–Vis absorption spectroscopy, X-ray diffraction (XRD), and transmission electron microscopy (TEM), along with assessing their antioxidant and antimicrobial properties against Gram-positive bacteria. The data collected from the experiments indicated that the nanoparticles were formed in a relatively short period of time (96 h) and, for the experimental variant involving the use of a 1:1 ratio (v/v, grape pomace extract: silver nitrate) for the nanoparticle phytosynthesis, the smallest crystallite sizes (from X-ray diffraction—4.58 nm and 5.14 nm) as well as spherical or semispherical nanoparticles with the lowest average diameters were obtained (19.99–23 nm, from TEM analysis). The phytosynthesis process was shown to enhance the antioxidant properties (determined using the DPPH assay) and the antimicrobial potential (tested against Gram-positive strains) of the nanoparticles, as evidenced by comparing their properties with those of the parent extracts; at the same time, the nanoparticles exhibited a selectivity in action, being active against the Staphylococcus aureus strain while presenting no antimicrobial potential against the Enterococcus faecalis strain.