Illicit supply chains for products like counterfeit Personal Protective Equipment (PPE) are characterized by sparse data and great uncertainty about the operational and logistical structure, making criminal activities largely invisible to law enforcement and challenging to intervene in. Simulation is a way to get insight into the behavior of complex systems, using calibration to tune model parameters to match its real-world counterpart. Calibration methods for simulation models of illicit supply chains should work with sparse data, while also tuning the structure of the simulation model. Thus, this study addresses the question: “To what extent can various model calibration techniques reconstruct the underlying structure of an illicit supply chain when varying the degree of data sparseness?” We evaluate the quality-of-fit of a reference technique, Powell's Method, and three model calibration techniques that have shown promise for sparse data: Approximate Bayesian Computing, Bayesian Optimization, and Genetic Algorithms. For this, we use a simulation model of a stylized counterfeit PPE supply chain as ground truth. We extract data from this ground truth and systematically vary its sparseness. We parameterize structural uncertainty using System Entity Structure. The results demonstrate that Bayesian Optimization and Genetic Algorithms are suitable for reconstructing the underlying structure of an illicit supply chain for a varying degree of data sparseness. Both techniques identify a diverse set of optimal solutions that fit with the sparse data. For a comprehensive understanding of illicit supply chain structures, we propose to combine the results of the two techniques. Future research should focus on developing a combined algorithm and incorporating solution diversity.