To speed up LTSpice simulations, users can change the integration method to trapezoidal, decrease the tolerance, and add large resistors in parallel with inductors. Reducing the simulation duration and recording less data can also enhance performance. The discussion highlights the importance of adjusting the time-step, especially when switching occurs on a microsecond scale for extended periods. Users are encouraged to evaluate the necessity of long simulation times. Implementing these strategies can significantly reduce simulation time.