AbstractWe address the resistance, somewhat pervasive within the sampling community, to model‐based methods. We do this by introducing notions of “approximate models” and then deriving sampling methods which are robust to model misspecification within neighbourhoods of the sampler's approximate, working model. Specifically we study robust sampling designs for model‐based stratification, when the assumed distribution of an auxiliary variable x, and the mean function and the variance function in the associated regression model, are only approximately specified. We adopt an approach of “minimax robustness,” to which end we introduce neighbourhoods of the “working” , and working regression model, and maximize the prediction mean squared error (MSE) for the empirical best predictor, of a population total, over these neighbourhoods. Then we obtain robust sampling designs, which minimize an upper bound of the maximum MSE through a modified genetic algorithm with “artificial implantation.” The techniques are illustrated in a case study of Australian sugar farms, where the goal is the prediction of total crop size, stratified by farm size. The Canadian Journal of Statistics 43: 554–577; 2015 © 2015 Statistical Society of Canada