One wouldn't want to count the number of scientific and engineering application areas where complex numerical simulators are now used. Many of these simulators rely on legacy codes and hence demand the use of derivative-free optimization algorithms, which treat the objective as a blackbox. In this talk I will discuss my recent efforts to unwrap some of these blackboxes to exploit the structure inherent in model calibration, parameter estimation, and synchronization problems (AKA nonlinear least squares). We extend our existing algorithm to one which builds an interpolating model for each of the simulator-dependent residuals. I'll show results supporting the improved efficiency of exploiting the structure of these problems and outline some directions of future research to solve ever-challenging problems.