Performing simulations with electromagnetic (EM) solvers can be a computationally complex task that is time consuming and resource demanding. Adaptive frequency sampling (AFS) techniques are very effective in reducing the computational complexity of frequency-domain simulations performed by EM solvers. In this work, we propose a novel AFS technique based on local rational models. This brings multiple advantages, such as accurate and efficient model uncertainty estimation, the local refinement of subintervals of the full frequency range of interest, and suitability toward parallel computing. Multiple numerical examples thoroughly validate the proposed technique. The local rational models can also be used as an accurate frequency-domain macromodeling technique after the AFS process is completed.