The light confinement properties of high quality (Q) factor microtoroid whispering-gallery mode (WGM) optical resonators prevent efficient coupling between far-field radiation and the WGM. Instead, light is most commonly evanescently coupled to the WGM using optical fibers that have been tapered to micron-scale thickness. These tapers, however, break easily and are sensitive to environmental vibrations and fluid flow fluctuations. This limits their effectiveness in mass-produced and/or field-portable biochemical sensing applications. Here we present a gold nanorod grating as an experimentally-feasible alternative for robust coupling of free-space light to a microtoroid resonator, and we simulate its performance with a novel finite-element 3D beam envelope method. 3D simulations of the full system are not tractable due to its large size. Previously, simulations of nanostructures on microtoroids have been performed on a thin wedge of the 3D system with perfect electrical conductor (mirror) boundary conditions. While these simulations provided some insight, they do not accurately model typical travelling-wave WGM experiments because they can only simulate standing waves. The standing wave nodes and antinodes significantly alter interactions between the WGM and the nanostructure. In our new method, we use a small wedge domain with custom boundary conditions that accurately simulate the travelling wave and nanophotonic interactions. Using this approach, we have designed and simulated a grating for far-field WGM coupling. With the grating, it is possible to maintain a high Q-factor of 3×10^6. We anticipate that our proposed modeling approach can solve a variety of other nanoparticle-microtoroid coupled systems in the future.