Built-up structures exhibit nonlinear dynamic phenomena due to friction at the surfaces that are held together using mechanical fasteners. This nonlinearity is hysteretic or history dependent. Additionally, interfacial slip results in stiffness and damping variations that are dependent on the vibration amplitude. In the microslip regime, the dissipation varies as a power of the amplitude. The four-parameter Iwan model can capture both the hysteretic and power-law dissipation behavior that is characteristic of many bolted joints. However, simulating the dynamic response of this model is computationally expensive since the states of several slider elements must be tracked implicitly, necessitating the use of fixed-step integration schemes with small time-steps. The Bouc–Wen model is an alternative hysteretic model in which the restoring force is given by a first-order nonlinear differential equation. Numerical integration of this model is much faster because it consists of just one additional state variable, i.e., the hysteretic variable. Existing literature predominantly focuses on studying the steady-state behavior of this model. This paper tests the effectiveness of the Bouc–Wen model in capturing power-law dissipation by comparing it to four-parameter Iwan models with various parameters. Additionally, the effect of each Bouc–Wen parameter on the overall amplitude-dependent damping is presented. The results show that the Bouc–Wen model cannot capture power-law behavior over the entire microslip regime, but it can be tuned to simulate the response over a smaller amplitude range.