An important research area in space physics and astrophysics is the transport of energetic, charged particles, such as electrons, protons, and muons, in magnetic turbulence, with active research in this field going back to Jokipii (1966). For example, the magnetic turbulence in the solar wind, arising from the combination of the motion of the solar wind plasma and the Sun's magnetic field, deflects energetic charged particles away from their initial trajectories. These particles may have originated in the Sun (solar energetic particles), or from sources outside the solar system such as supernova remnants (galactic cosmic rays) or active galactic nuclei (extra-galactic cosmic rays). Regardless of their origin, these high energy particles will be deflected in the heliospheric magnetic field, with transport being described by diffusion coefficients parallel and perpendicular to the local mean field. Research over the years has shown that the perpendicular transport needs to be described by theoretical models that are highly non-linear. Test-particle simulations performed using various analytical turbulence models have allowed these theoretical descriptions of particle transport to be improved by providing numerical results to compare with theoretical predictions. In this work, a test-particle code has been developed using a new trajectory solver that allows for better energy conservation and position accuracy. This is then used in simulations performed to test the predictions of theory in the limit of small Kubo number turbulence.