Finding new techniques to accelerate electromagnetic (EM) simulations has become a necessity nowadays due to its frequent usage in industry. As they are mainly based on domain discretization, EM simulations require solving enormous systems of linear equations simultaneously. Available software-based solutions do not scale well with the increasing number of equations to be solved. As a result, hardware accelerators ave been utilized to speed up the process. We introduce using hardware emulation as an efficient solution for EM simulation core solvers. Two different scalable architectures are implemented to accelerate the solver part of an EM simulator based on the Gaussian Elimination and the Jacobi iterative methods. Results show that the performance gap between presented solutions and software-based ones increases as the number of equations increases. For example, solving 2,002,000 equations using our Clustered Jacobi design in single floating-point precision achieved a speed-up of 100.88x and 35.24x over pure software implementations represented by MATLAB and the ALGLIB C++ package, respectively.