Environmental policy evaluation is characterised by a paucity of information. Bounded sets may be more appropriate for representing this ambiguity than traditional probability distributions. A formal calibration method for regional policy models, positive mathematical programming, is thus extended to incorporate parameter definition using bounded sets through the novel method of robust non-linear programming. The resulting procedure identifies strong bounds on the range of abatement costs accruing to environmental policy and improves the relevance and value of modelling studies through not limiting conclusions to realisations of specific point estimates or probability distributions. Moreover, it may easily be solved using standard mathematical-programming algorithms. Empirical insights are provided in an application to a New Zealand inland lake threatened by nitrate pollution from dairy farming. Factor substitution could potentially be used to reduce the abatement costs accruing to regulation. However, such behaviour is shown not to be optimal at the parameter values used in this study. Accordingly, large reductions in nitrate leaching and concomitant improvements in water quality potentially bear a substantial cost to producers.