A passive vibration isolator using a negative stiffness mechanism (NSM) is being considered for small precision instruments since it does not need any outer power supply and pressurized air, and its fundamental frequency can be lowered down to 0.5 Hz. Although the working principle of the NSM and its patents are well known, neither the isolation performance limit related to the lowest fundamental frequency nor its nonlinear behavior have been studied. This paper discusses the performance limit of the passive vertical isolator using the NSM and presents the design guidelines for the isolator based on that performance limit. First, a nonlinear dynamic model of the passive isolator is derived through solid approximations, and the fundamental frequency or performance limit is obtained using nonlinear analysis, which entirely explains the nonlinear behavior of the isolator. In addition, the approximate design equations of the isolator are derived to analyze its performance limit. Finally, an approximate expression of the lowest fundamental frequency of the isolator is derived using nonlinear analysis and design equations, which provide substantial design guidelines to improve isolator performance.