Astrophysical observations suggest that magnetic reconnection in relativistic plasmas plays an important role in the acceleration of energetic particles. Modeling this accurately requires numerical schemes capable of addressing large scales and realistic magnetic field configurations without sacrificing the kinetic description needed to model particle acceleration self-consistently. We demonstrate the computational advantage of the relativistic semi-implicit method (RelSIM), which allows for reduced resolution while avoiding the numerical instabilities typically affecting standard explicit methods, helping to bridge the gap between macroscopic and kinetic scales. Two- and three-dimensional semi-implicit particle-in-cell simulations explore the linear tearing instability and the nonlinear development of reconnection and subsequent particle acceleration starting from a relativistic Harris equilibrium with no guide field. The simulations show that particle acceleration in the context of magnetic reconnection leads to energetic power-law spectra with cutoff energies, consistent with previous work done using explicit methods, but are obtained with a considerably reduced resolution.