Luminous infrared (IR) galaxies are key sites of obscured stellar mass assembly at z > 0.5. Their star formation rates (SFRs) are often estimated using the luminosities of the 6.2 and 11.2 μm polycyclic aromatic hydrocarbon (PAH) features or those of the [Ne II] and [Ne III] fine-structure lines, as they are minimally affected by obscuration. It is uncertain whether the calibration of these features as SFR tracers depends on the starburst bolometric luminosity or the level of active galactic nucleus (AGN) activity. We here investigate the relationship between the luminosities of PAH and neon lines with SFR for highly luminous objects using radiative transfer modeling and archival observations of 42 local ultraluminous (≥1012L⊙) IR galaxies (ULIRGs). We find that PAH and [Ne II] features arise mainly in star-forming regions, with small contributions from the AGN or host, but that the [Ne III] line has a mixed contribution from both star formation and AGN activity. We present relations between LPAH and L[Ne II], and both starburst luminosity and SFR. We find relations for lower-luminosity (LIR ≃ 1010─1012L⊙) systems underestimate the SFRs in local ULIRGs by up to ∼1 dex. The 6.2 and 11.2 μm PAH features, and the [Ne II] line, are thus good tracers of SFR in ULIRGs. We do not find that a more luminous AGN affects the relationship between SFR and PAH or neon luminosity but that it can make PAH emission harder to discern. Our results and derived relations are relevant to studies of star-forming and composite galaxies at z < 3 with the James Webb Space Telescope.