We examine procedures for declaring an area free of pest fruit flies following an eradication campaign. To date, the acceptable period of trapping zero flies has been calculated without an estimate of the probability of being wrong. The zero trapping periods are usually shorter when declaring local ‘area freedom’ from an endemic fly, than when claiming eradication of an exotic species. We use a model to calculate the probability of zero trap captures and therefore the probability of trapping further flies. The latter probability is always finite. A zero trapping result does not indicate the absence of flies. There must also be evidence of what constitutes a non-viable density, as indicated by the trapping rate. The non-viable densities of certain pest fruit fly species are known from decades of managing small incursions in fly-free zones. There is no need for implementation of eradication procedures if the trapping rate is sufficiently low, in these areas. For a given density of flies (defined in terms of expected mean catch per trap per week), the probability of zero trap captures reduces with time and the number of traps employed. If the model calculations use a non-sustainable density (inferred from trapping rate) then we may declare the actual density of flies to be less if the trapping result is zero for a given number of weeks with a given number of traps when the model predicts the probability of such a result to be sufficiently low, according to a criterion that is selected at a level suited to the purpose of the declaration.