Advancements in data collection and high performance computing are making sophisticated model calibration possible throughout the modeling and simulation community. The model calibration process, in which the appropriate input values are estimated for unknown parameters, is typically a computationally intensive task and necessitates the use of distributed software components. These components are often heterogeneous due to the combination of the model and the optimization software, making scalability difficult to achieve. We have developed a hybrid software system for parameter estimation consisting of an optimization algorithm implemented in a mathematical scripting language, a legacy Fortran model, and an MPI client program. Through a series of optimizations, we achieved near-linear speedup when the model is executed as a standalone process, and achieved superlinear speedup when the model is executed as a subroutine. We report on our optimization techniques and performance results of an estimation problem within the context of an ongoing modeling study.