Summary: Site occupancy, as estimated by the probability of presence, is used for monitoring species populations. However, the detection of species at individual sites is often subject to errors. In order to accurately estimate occupancy we must simultaneously account for imperfect detectability by estimating the probability of detection. The problem with estimating occupancy arises from not knowing whether a nondetection occurred at an occupied site due to imperfect detectability (sampling zeros), or the nondetection resulting from an unoccupied site (fixed zeros). We evaluated the performance of the basic, normal approximation, studentised and percentile methods for approximating confidence limits for occupancy and detection of species. Using coverage and average interval width, we demonstrated that the studentised estimator was generally superior to the others, except when a small sample of sites are selected. Under this circumstance and when calculating limits for detection, no estimator produced reliable results. The experimental factors we considered include: (i) number of sites; (ii) number of survey occasions; (iii) probabilities of presence (occupancy) and detection; and (iv) overdispersion in the capture matrix. Similar conclusions were reached both for the simulated studies and a case study. Overall, estimation near the boundaries of the probability of occupancy and detectability was difficult.