Outflows are a pervasive feature of mechanical feedback from super star clusters (SSC) in starburst galaxies, playing a fundamental role in galaxy evolution. Observations are now starting to confirm that outflows can undergo catastrophic cooling, suppressing adiabatic superwinds. Here we present a suite of one-dimensional, hydrodynamic simulations that study the ionization structure of these outflows and the resulting line emission generated by the cooling gas. We use the non-equilibrium atomic chemistry package within MAIHEM, our modified version of FLASH, which evolves the ionization state of the gas and computes the total cooling rate on an ion-by-ion basis. We find that catastrophically cooling models produce strong nebular line emission compared to adiabatic outflows. We also show that such models exhibit non-equilibrium conditions, thereby generating more highly ionized states than equivalent equilibrium models. When including photoionization from the parent SSC, catastrophically cooling models show strong C IV {lambda}1549 and O VI {lambda}1037 emission. For density bounded photoionization, He II {lambda}1640, {lambda}4686, C III] {lambda}1908, Si IV {lambda}1206, and Si III {lambda}1400 are also strongly enhanced. These lines are seen in extreme starbursts where catastrophic cooling is likely to occur, suggesting that they may serve as diagnostics of such conditions. The higher ionization generated by these flows may help to explain line emission that cannot be attributed to SSC photoionization alone.