Estimation of animal density is fundamental to wildlife research and management, but estimation via mark–recapture is often complicated by lack of geographic closure of study sites. Contemporary methods for estimating density using mark–recapture data include (1) approximating the effective area sampled by an array of detectors based on the mean maximum distance moved (MMDM) by animals during the sampling session, (2) spatially explicit capture–recapture (SECR) methods that formulate the problem hierarchically with a process model for animal density and an observation model in which detection probability declines with distance from a detector, and (3) a telemetry estimator (TELEM) that uses auxiliary telemetry information to estimate the proportion of animals on the study site. We used simulation to compare relative performance (percent error) of these methods under all combinations of three levels of detection probability (0.2, 0.4, 0.6), three levels of occasions (5, 7, 10), and three levels of abundance (10, 20, 40 animals). We also tested each estimator using five different models for animal home ranges. TELEM performed best across most combinations of capture probabilities, sampling occasions, true densities, and home range configurations, and performance was unaffected by home range shape. SECR outperformed MMDM estimators in nearly all comparisons and may be preferable to TELEM at low capture probabilities, but performance varied with home range configuration. MMDM estimators exhibited substantial positive bias for most simulations, but performance improved for elongated or infinite home ranges.