We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (GR-RMHD) equations within the Whisky code. The numerical method adopted exploits the properties of Implicit-Explicit Runge-Kutta (RKIMEX) numerical schemes to treat the stiff terms of the equations. We report simulations of magnetized non-rotating stars both in the Cowling approximation and in dynamical spacetimes. In addition, the case of a collapsing non-rotating star has been studied because it provides a very good testbed for numerical codes with dynamical electromagnetic fields in strong gravity and because of its astrophysical relevance. We show that our results are in good agreement with the perturbative studies of the dynamics of electromagnetic fields in a Schwarzschild background.