Project 8 aims to measure neutrino mass using a method that is conceptually straightforward but technologically challenging. The operating principle is to put tritium in a uniform magnetic field, causing the emitted electron to undergo cyclotron motion and radiate. Measuring the electron's radiation frequency yields its energy, and the energy spectrum constrains the mass of the neutrino involved in the decay. This method has worked in a small waveguide, but to improve neutrino mass sensitivity it needs to be demonstrated in a large free-space volume. The next phase of this experiment will be done in a medical MRI magnet with an array of antennas viewing the tritium volume. Detection is challenging because a single electron emits $<$1 fW at $\sim$26 GHz. This poster shows how high-frequency simulations of this complex system have driven design progress in the antenna, cryogenic, and mechanical subsystems.