We present a new methodology for simulating mid-infrared emission from polycyclic aromatic hydrocarbons (PAHs) in galaxy evolution simulations. To do this, we combine theoretical models of PAH emission features as they respond to varying interstellar radiation fields, grain-size distributions, and ionization states with a new model for dust evolution in galaxy simulations. We apply these models to three idealized arepo galaxy evolution simulations within the smuggle physics framework. We use these simulations to develop numerical experiments investigating the buildup of PAH masses and luminosities in galaxies in idealized analogs of the Milky Way, a dwarf galaxy, and a starburst disk. Our main results are as follows. Galaxies with high specific star formation rates have increased feedback energy per unit mass, and are able to shatter grains efficiently, driving up the fraction of ultrasmall grains. At the same time, in our model large radiation fields per unit gas density convert aliphatic grains into aromatics. The fraction of dust grains in the form of PAHs (q _PAH) can be understood as a consequence of these processes, and in our model PAHs form primarily from interstellar processing (shattering) of larger grains rather than from the growth of smaller grains. We find that the hardness of the radiation field plays a larger role than variations in the grain-size distribution in setting the total integrated PAH luminosities, though cosmological simulations are necessary to investigate fully the complex interplay of processes that drive PAH band luminosities in galaxies.