As computational models have improved in fidelity and increased in complexity, surrogate-based optimization has become increasingly important. Surrogates, or response surface models, are often used to decrease the total computational cost of finding an optimal design point and make a problem computational tractable. In addition, they may be used to guide the optimal search process. In this talk, we will focus on the problem of model calibration (i.e. the process of inferring the values of model parameters so that the results of the simulations best match observed behavior), and describe how surrogates can be also be used to incorporate parameter sensitivity information. The resulting new algorithm is a hybrid of traditional optimization and statistical analysis techniques that presents the user with a choice of solutions and corresponding confidence intervals. We will describe the methodology, discuss its open source software implementation, and give some results for calibration problems from electrical and mechanical engineering.