With excellent spectral and angular resolutions and, especially, sensitivity, the JWST allows us to observe infrared emission lines that were previously inaccessible or barely accessible. These emission lines are promising for evaluating the physical conditions in different galaxies. Based on MAPPINGS V photoionization models, we systematically analyze the dependence of over 20 mid-infrared (mid-IR) emission lines covered by MIRI on board JWST on the physical conditions of different galactic environments, in particular narrow-line regions in active galactic nuclei (AGN). We find that mid-IR emission lines of highly ionized argon (i.e., [Ar V] 7.90 and 13.10 μm) and neon (i.e., [Ne V] 14.32 and 24.32 μm, and [Ne VI] 7.65 μm) are effective in diagnosing the physical conditions in AGN. We accordingly propose new prescriptions to constrain the ionization parameter (U), peak energy of the AGN spectrum (Epeak), metallicity ( 12+log(O/H) ), and gas pressure (P/k) in AGN. These new calibrations are applied to the central regions of six Seyfert galaxies included in the Galaxy Activity, Torus, and Outflow Survey as a proof of concept. We also discuss the similarity and difference in the calibrations of these diagnostics in AGN of different luminosities, highlighting the impact of hard X-ray emission and particularly radiative shocks, as well as the different diagnostics in star-forming regions. Finally, we propose diagnostic diagrams involving [Ar V] 7.90 μm and [Ne VI] 7.65 μm to demonstrate the feasibility of using the results of this study to distinguish galactic regions governed by different excitation sources.