This paper focuses on microwave power (180, 300, 450, 600 and 800 W) effect on the quality and composition of rosemary leaves essential oils obtained by solvent-free microwave extraction (SFME). The results were compared to the effect of conventional hydrodistillation (HD). The analyses revealed 29 compounds for all extracts. α-pinene, camphor, borneol and (E)-caryophyllene were the major constituents, depending on extraction parameters. The antioxidant assay showed that the lowest value of the median inhibitory concentration (IC50) was for SFME 180. The statistical assessment allowed the possibility to distinguish a new simple approach to evaluate the synergistic and antagonistic effects between essential oils constituents on the antiradical activity. Results exhibit the interest in microwave power impact on essential oils extraction. This constitutes the novelty of this study, which is the possibility of improving the quality of the extract by adjusting the abundance of target compounds characterized by a strong antioxidant effect.