The increasing operation speed of high-speed trains allows the pantograph to continuously interact with the catenary over a long distance in a short time, and many new methods have been developed to efficiently calculate its dynamics. However, the existing methods only consider simple catenary systems, which limits their application in high-speed railway systems. In this work, a reduced pantograph–stitched-catenary interaction model is developed to simulate pantograph–stitched-catenary interactions during long-distance travel. Based on the existing reduced catenary model, the stitched catenary system is first considered, where the stitched wire is simplified into a part of the messenger wire supported by two spring-damping elements. The present model is validated by test results and the EN 50318:2018 standard, and it is subsequently used to study the dynamic performance of the pantograph–stitched-catenary system at an overdesigned speed in Sweden. The results show that the proposed model can be seven times faster than the traditional modal superposition method with the same accuracy in a stitched catenary system, and the existing catenary system cannot be operated at an overdesigned speed without increasing the contact wire tension. The present model gives an efficient solution to pantograph–stitched-catenary interaction problems.