Environmental DNA (eDNA) sampling is a promising method for surveying aquatic fauna. Recent eDNA studies have investigated the likelihood of false negative errors in the laboratory and in the field, but the likelihood of false positives remains poorly studied. We investigated the likelihood of both types of errors in eDNA surveys of an Australian threatened freshwater fish (Galaxiella pusilla) using laboratory experiments, field surveys, and recent advances in hierarchical site occupancy‐detection modeling. Laboratory experiments revealed high primer/probe specificity; absence of sample contamination in extraction and qPCR blanks; and rapid accumulation and deterioration of eDNA in aquaria. Hierarchical site occupancy‐detection models fitted to pilot data collected at 13 wetlands revealed that two water samples, each with two qPCRs, would be required to achieve a cumulative detection probability >.95. A more comprehensive survey, in which we simultaneously used dip netting and eDNA sampling at 29 wetlands, revealed similar mean detection probabilities of the two sampling methods (trapping: 0.74 vs. eDNA: 0.68), and low probabilities of false positive errors at the water sample level (0.0080) and at the qPCR level (0.0039) for eDNA sampling. Collectively, our results illustrate that eDNA sampling can be a sensitive and specific method for monitoring the occurrence of freshwater fauna. Detection probabilities of eDNA sampling were comparable to those of a traditional sampling method, and probabilities of laboratory‐induced false positives were low. Future studies employing eDNA sampling should estimate, and properly account for, false positive errors in addition to false negatives.