Numerical simulations of the propagation of charged particles through magnetic fields solving the equation of motion often leads to the usage of an interpolation in the case of discretely defined magnetic fields, typically given on a homogeneous grid structure. However, the interpolation method influences the magnetic field properties and, therefore, also the propagation of particles through these fields. To determine the resulting error, we compare three different interpolation routines-trilinear, tricubic, and nearest neighbor interpolation-in the case of isotropic, turbulent magnetic fields. First, we analyze the impact of the different interpolation methods on the root mean square field strength, the divergence, and the spectrum of the turbulent magnetic field. Here, the nearest neighbor interpolation shows some clear benefits compared with the trilinear method; however, that changes significantly if we consider the particle propagation. In principle, a better interpolation method also yields a better description of the particle transport. In the case of field line random walk, it is shown that none of these methods, especially not the nearest neighbor interpolation, is able to yield an accurate description of the diffusion coefficient, exposing the need for a continuous, grid-less turbulent magnetic field. We optimize the performance of an algorithm that generates such a magnetic field by more than an order of magnitude. Further, the necessary number of wave-modes is determined, so that this continuous method supports realistic simulations over a larger energy range without limitations by the available memory.