The volatiles of different aerial parts of three kumquat species (Fortunella margarita Swingle–Nagami, Fortunella japonica Swingle–Marumi, and Fortunella crassifolia Swingle–Meiwa) growing in Greece were analyzed via GC-MS and evaluated for their antimicrobial properties against nine human pathogenic microorganisms. A total number of 23 compounds were identified in the peel, 38 in the leaves, and 30 in the flowers of the examined species. Limonene was the dominant metabolite in the peels of all three species, germacrene-D was present in the leaves of Nagami and Marumi kumquats, while limonene was the most abundant in the flower of Marumi and Meiwa kumquat but with significant differences in the composition of the total fracture of the essential oil, since compounds with high antimicrobial activity were only present in the flower of Meiwa kumquat. The essential oils from the leaf and peel of the three kumquat species were either inactive or showed weak antimicrobial activity, respectively, against Gram-positive and Gram-negative bacterial strains and pathogenic fungi. Only the essential oil from the flower of F. crassifolia Swingle (Meiwa) showed a stronger effect (MIC values 3.5–7.48 mg/mL) against all the assayed microorganisms. Furthermore, through multivariate statistical analysis, we studied the relationships between the samples regarding their origin (species and plant part), as well as between the chemical composition of the corresponding essential oils and their antimicrobial activity. Considering its chemical profile and antimicrobial activity, the Greek Meiwa flowers’ essential oil seemed a promising essential oil for further exploitation in the food and/or medicinal industry.