Numerical models to simulate interface behavior of friction connections under cyclic loading are investigated. The question of validity of lower-order models in successfully capturing response of friction joints under cyclic loading is addressed. Single-element macroslip models are not capable of capturing localized interface behavior prior to gross interfacial slip. This paper focuses on the convergence behavior of a multipoint contact microslip model comprised of Iwan-type elements for different physical parameters such as system response amplitude and kinematic state of the friction joint. System dynamics play a significant role in determining the convergence of structural behavior, especially for tuned damper sets in the nonzero damper mass case. This behavior is explored using simple linearized models that explain the response sensitivity in terms of the overall modal density near the forcing frequency. Convergence of the interface response kinematics is also considered, with a focus on the number of damping elements operating in the stick, stick-slip, and slip regimes at steady state. Energy dissipation scaling under light forcing is also examined, with the class of models considered here yielding scaling exponents consistent with experimental observations and analytical predictions from the literature. We show that the interface kinematic behavior converges at a slower rate than the structural response and therefore requires a higher-order interface model. These results suggest that extremely low-order models (i.e., damping elements) provide predictions that are model order dependent, while higher-order models (i.e., damping elements) are not. This result impacts model development and calibration approaches, as well as providing clues for appropriate model reduction strategies.