Network intrusion detection systems (NIDS) are commonly used to detect malware communications, including command-and-control (C2) traffic from botnets. NIDS performance assessments have been studied for decades, but mathematical modeling has rarely been used to explore NIDS performance. This paper details a mathematical model that describes a NIDS performing packet inspection and its detection of malware's C2 traffic. The paper further describes an emulation testbed and a set of cyber experiments that used the testbed to validate the model. These experiments included a commonly used NIDS (Snort) and traffic with contents from a pervasive malware (Emotet). Results are presented for two scenarios: a nominal scenario and a “stressed” scenario in which the NIDS cannot process all incoming packets. Model and experiment results match well, with model estimates mostly falling within 95 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> confidence intervals on the experiment means. Model results were produced 70-3000 times faster than the experimental results. Consequently, the model's predictive capability could potentially be used to support decisions about NIDS configuration and effectiveness that require high confidence results, quantification of uncertainty, and exploration of large parameter spaces. Furthermore, the experiments provide an example for how emulation testbeds can be used to validate cyber models that include stochastic variability.