Testing is critical to mitigating the COVID-19 pandemic, but testing capacity has fallen short of the need in the United States and elsewhere, and long wait times have impeded rapid isolation of cases. Operational challenges such as supply problems and personnel shortages have led to these bottlenecks and inhibited the scale-up of testing to needed levels. This paper uses operational simulations to facilitate rapid scale-up of testing capacity during this public health emergency. Specifically, discrete event simulation models were developed to represent the RT-PCR testing process in a large University of Maryland testing center, which retrofitted high-throughput molecular testing capacity to meet pandemic demands in a partnership with the State of Maryland. The simulation models support analyses that identify process steps which create bottlenecks, and evaluate "what-if" scenarios for process changes that could expand testing capacity. This enables virtual experimentation to understand the trade-offs associated with different interventions that increase testing capacity, allowing the identification of solutions that have high leverage at a feasible and acceptable cost. For example, using a virucidal collection medium which enables safe discarding of swabs at the point of collection removed a time-consuming "deswabbing" step (a primary bottleneck in this laboratory) and nearly doubled the testing capacity. The models are also used to estimate the impact of demand variability on laboratory performance and the minimum equipment and personnel required to meet various target capacities, assisting in scale-up for any laboratories following the same process steps. In sum, the results demonstrate that by using simulation modeling of the operations of SARS-CoV-2 RT-PCR testing, preparedness planners are able to identify high-leverage process changes to increase testing capacity.