We consider the construction of robust sampling designs for the estimation of threshold probabilities in spatial studies. A threshold probability is a probability that the value of a stochastic process at a particular location exceeds a given threshold. We propose designs which estimate a threshold probability efficiently, and also deal with two possible model uncertainties: misspecified regression responses and misspecified variance/covariance structures. The designs minimize a loss function based on the relative mean squared error of the predicted values (i.e., relative to the true values). To this end an asymptotic approximation of the loss function is derived. To address the uncertainty of the variance/covariance structures of this process, we average this loss over all such structures in a neighbourhood of the experimenter's nominal choice. We then maximize this averaged loss over a neighbourhood of the experimenter's fitted model. Finally the maximum is minimized, to obtain a minimax design.