Self-induced mechanical oscillation of nose landing gears designated as shimmy is a major safety challenge for aircrafts. The rotational-lateral shimmy vibrations can occur during takeoff, taxiing, and landing and needs to be sufficiently controlled to avoid escalation and catastrophic failure of the landing gear system. Existing solutions for shimmy problem are largely passive control strategies known as shimmy dampers. Despite numerous studies on the source of shimmy and its trends, investigations on the design and performance analysis of shimmy dampers are scarce. From a design perspective, it is crucial to quantify the effective stiffness and damping supplied by the shimmy damper to the system in different operation states. Furthermore, the sensitivity of the damper performance to its design parameters needs to be thoroughly investigated in order to optimize the design for a particular aircraft. In this study, core relationships for three shimmy dampers are presented and used to perform sensitivity studies. These dampers are concepts by Boeing, Collins Aerospace (formerly UTAS), and a new one designated as the Symmetric Torque Link Damper (STLD). The influence of design parameters on the dampers’ performance is studied and observed trends are discussed in the light of inherent trade-offs. Subsequently, a nonlinear Multibody Dynamic model of the landing gear is utilized to obtain sample time histories of oscillations for each shimmy damper in order to highlight the performance differences and to demonstrate the influence of design parameters. Directions for designing future shimmy dampers and recommendations for optimizing them are offered.