Microsimulation models (MSMs) are used to predict population-level effects of health care policies by simulating individual-level outcomes. Simulated outcomes are governed by unknown parameters that are chosen so that the model accurately predicts specific targets, a process referred to as model calibration. Calibration targets can come from randomized controlled trials, observational studies, and expert opinion, and are typically summary statistics. A well calibrated model can reproduce a wide range of targets. MSM calibration generally involves searching a high dimensional parameter space and predicting many targets through model simulation. This requires efficient methods for exploring the parameter space and sufficient computational resources. We develop Incremental Mixture Approximate Bayesian Computation (IMABC) as a method for MSM calibration and implement it via a high-performance computing workflow, which provides the necessary computational scale. IMABC begins with a rejection-based approximate Bayesian computation (ABC) step, drawing a sample of parameters from the prior distribution and simulating calibration targets. Next, the sample is iteratively updated by drawing additional points from a mixture of multivariate normal distributions, centered at the points that yield simulated targets that are near observed targets. Posterior estimates are obtained by weighting sampled parameter vectors to account for the adaptive sampling scheme. We demonstrate IMABC by calibrating a MSM for the natural history of colorectal cancer to obtain simulated draws from the joint posterior distribution of model parameters.