Numerical solutions of electromagnetic problems involving nanostructures at terahertz (THz) frequencies are considered. We particularly focus on nanoparticles that are made of typical metals at the lower THz frequencies. Even though the frequency is relatively low, we show that penetrable models are needed for accurately representing electromagnetic characteristics, especially to predict penetrating magnetic fields inside small particles. Due to large permittivity values with negative real parts, stable formulations are needed to obtain equivalent currents and secondary fields. It is shown that the modified combined tangential formulation, which was proposed for plasmonic simulations in wide frequency ranges, provides accurate solutions that are consistent with analytical results for spherical nanoparticles.