A purely software-based approach for Real-Time Simulation (RTS) may have difficulties in meeting real-time constraints for complex physical model simulations. In this paper, we present a methodology for the design and implementation of RTS algorithms, based on the use of Field-Programmable Gate Array (FPGA) technology to improve the response time of these models. Our methodology utilizes traditional hardware/software co-design approaches to generate a heterogeneous architecture for an FPGA-based simulator. The hardware design was optimized such that it efficiently utilizes the parallel nature of FPGAs and pipelines the independent operations. Further enhancement is obtained through the use of custom accelerators for common non-linear functions. Since the systems we examined had relatively low response time requirements, our approach greatly simplifies the software components by porting the computationally complex regions to hardware. We illustrate the partitioning of a hardware-based simulator design across dual FPGAs, initiate RTS using a system input from a Hardware-in-the-Loop (HIL) framework, and use these simulation results from our FPGA-based platform to perform response analysis. The total simulation time, which includes the time required to receive the system input over a socket (without HIL), software initialization, hardware computation, and transfer of simulation results back over a socket, shows a speedup of 2x as compared to a similar setup with no hardware acceleration. The correctness of the simulation output from the hardware has also been validated with the simulated results from the software-only design.