Environmental DNA (eDNA) metabarcoding is increasingly used to study the present and past biodiversity. eDNA analyses often rely on amplification of very small quantities or degraded DNA. To avoid missing detection of taxa that are actually present (false negatives), multiple extractions and amplifications of the same samples are often performed. However, the level of replication needed for reliable estimates of the presence/absence patterns remains an unaddressed topic. Furthermore, degraded DNA and PCR/sequencing errors might produce false positives. We used simulations and empirical data to evaluate the level of replication required for accurate detection of targeted taxa in different contexts and to assess the performance of methods used to reduce the risk of false detections. Furthermore, we evaluated whether statistical approaches developed to estimate occupancy in the presence of observational errors can successfully estimate true prevalence, detection probability and false-positive rates. Replications reduced the rate of false negatives; the optimal level of replication was strongly dependent on the detection probability of taxa. Occupancy models successfully estimated true prevalence, detection probability and false-positive rates, but their performance increased with the number of replicates. At least eight PCR replicates should be performed if detection probability is not high, such as in ancient DNA studies. Multiple DNA extractions from the same sample yielded consistent results; in some cases, collecting multiple samples from the same locality allowed detecting more species. The optimal level of replication for accurate species detection strongly varies among studies and could be explicitly estimated to improve the reliability of results.