Direct time-domain simulation of continuous-wave (CW) EPR spectra from molecular dynamics (MD) trajectories has become increasingly popular, especially for proteins labeled with nitroxide spin labels. Due to the time-consuming nature of simulating adequately long MD trajectories, two approximate methods have been developed to reduce the MD trajectory length required for modeling EPR spectra: hindered Brownian diffusion (HBD) and hidden Markov models (HMMs). Here, we assess the accuracy of these two approximate methods relative to direct simulations from MD trajectories for three spin-labeled protein systems (a simple helical peptide, a soluble protein, and a membrane protein) and two nitroxide spin labels with differing mobilities (R1 and TOAC). We find that the HMMs generally outperform HBD. Although R1 dynamics partially resembles hindered Brownian diffusion (HBD), HMMs accommodate the multiple dynamic timescales for the transitions between rotameric states of R1 that cannot be captured accurately by a HBD model, even when a three-angle orientational potential and recently developed estimation methods for the rotational diffusion tensor are utilized. We show that TOAC dynamics closely resembles slow multi-site exchange between twist-boat and chair ring puckering states, and we establish for the first time that this motion is modeled well by a HMM with up to four states, but not by HBD. All MD trajectory data processing, stochastic trajectory simulations, and CW EPR spectral simulations are implemented in EasySpin, a free software package for MATLAB.