In vaccine efficacy trials, inaccurate counting of infection cases leads to systematic under-estimation—or “dilution”—of vaccine efficacy. In particular, if a sufficient fraction of observed cases are false positives, apparent efficacy will be greatly reduced, leading to unwarranted no-go decisions in vaccine development. Here, we propose a range of replicate testing strategies to address this problem, considering the additional challenge of uncertainty in both infection incidence and diagnostic assay specificity/sensitivity. A strategy that counts an infection case only if a majority of replicate assays return a positive result can substantially reduce efficacy dilution for assays with non-systematic (i.e., “random”) errors. We also find that a cost-effective variant of this strategy, using confirmatory assays only if an initial assay is positive, yields a comparable benefit. In clinical trials, where frequent longitudinal samples are needed to detect short-lived infections, this “confirmatory majority rule” strategy can prevent the accumulation of false positives from magnifying efficacy dilution. When widespread public health screening is used for viruses, such as SARS-CoV-2, that have non-differentiating features or may be asymptomatic, these strategies can also serve to reduce unneeded isolations caused by false positives.