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We examine the sensitivity of simple calibration models of trade in imperfectly competitive industries to changes in model specification, as well as to changes in the calibration parameters. We find that not just the magnitude, but also the sign of the optimal trade policies is very sensitive to the change in model specification. Indeed, use of policies derived from the 'wrong' model can reduce welfare from the status quo. However, the welfare gains to be obtained from application of the 'correct' model remain limited. Calibration models nonetheless provide useful estimates of firm and market behavior over time, as well as disaggregated elasticities of demand. We conclude that careful empirical work is necessary to guide model selection. For the present, the case for activist trade policy on the basis of calibration models should not be made.