Statements of extinction will always be uncertain because of imperfect detection of species in the wild. Two errors can be made when declaring a species extinct. Extinction can be declared prematurely, with a resulting loss of protection and management intervention. Alternatively, limited conservation resources can be wasted attempting to protect a species that no longer exists. Rather than setting an arbitrary level of certainty at which to declare extinction, we argue that the decision must trade off the expected costs of both errors. Optimal decisions depend on the cost of continued intervention, the probability the species is extant, and the estimated value of management (the benefit of management times the value of the species). We illustrated our approach with three examples: the Dodo (Raphus cucullatus), the Ivory-billed Woodpecker (U.S. subspecies Campephilus principalis principalis), and the mountain pygmy-possum (Burramys parvus). The dodo was extremely unlikely to be extant, so managing and monitoring for it today would not be cost-effective unless the value of management was extremely high. The probability the Ivory-billed woodpecker is extant depended on whether recent controversial sightings were accepted. Without the recent controversial sightings, it was optimal to declare extinction of the species in 1965 at the latest. Accepting the recent controversial sightings, it was optimal to continue monitoring and managing until 2032 at the latest. The mountain pygmy-possum is currently extant, with a rapidly declining sighting rate. It was optimal to conduct as many as 66 surveys without sighting before declaring the species extinct. The probability of persistence remained high even after many surveys without sighting because it was difficult to determine whether the species was extinct or undetected. If the value of management is high enough, continued intervention can be cost-effective even if the species is likely to be extinct.