The real-time monitoring of the structural displacement of the vacuum vessel of thermonuclear fusion devices caused by electromagnetic loads is of great interest. In this paper, model order reduction is applied to the integral equation methods and the finite elements method to develop electromagnetic and structural reduced order models (ROMs) compatible with real-time execution which allows for the real-time monitoring of strain and displacement in critical positions of Tokamaks machines. Low-rank compression techniques based on hierarchical matrices are applied to reduce the computational cost during the offline stage when the ROMs are constructed. Numerical results show the accuracy of the approach and demonstrate the compatibility with real-time execution in standard hardware.