Achieving low absolute pressures is required in many industrial applications and remains a significant challenge in fluid engineering, particularly when compact and economically viable vacuum-generation systems are required for practical industrial applications. To achieve such low pressures, either high-capacity vacuum pumps must be employed, which may not be cost-effective due to their high procurement and maintenance costs, or multistage ejector vacuum supply systems must be used, which can substantially increase the overall system dimensions. A combined ejector–vacuum pump system consists of an ejector coupled with a vacuum pump and offers two main advantages. First, it prevents excessive increases in the dimensions of the vacuum supply system, as occurs in multistage ejector systems under demanding operating conditions. Second, it reduces the pressure load imposed on the vacuum pump compared with a system based solely on a vacuum pump, thereby enabling the use of a lower-capacity vacuum pump. In this configuration, a supersonic air ejector initially generates the required vacuum, in the range of a few millibars absolute, while increasing the pressure at the ejector outlet to several hundred millibars. The outlet flow from the ejector diffuser subsequently enters the vacuum pump, completing the vacuum generation process. In this study, the optimum operating point of the ejector–vacuum pump combination is determined from the intersection of the pressure–flowrate characteristic curves of the ejector and the corresponding vacuum pump. Based on this methodology, a combined ejector–vacuum pump system was designed and evaluated to provide a vacuum pressure of 40 mbar at a flow rate of 0.01 kg/s using a one-dimensional gas-dynamics model. The results demonstrate that the MATLAB code developed for the one-dimensional gas-dynamics model of the supersonic air ejector has an error of less than 3% compared with experimental results, confirming its capability to accurately model the ejector vacuum supply system with satisfactory accuracy.