In light of its empirical undetectability, physicists have attempted to establish Hawking radiation as universal-as a phenomenon that should appear regardless of the possible details of quantum gravity, whatever those details might be. But, as pointed out in a recent article by Gryb, Palacios, and Thébault (2019), these universality arguments for Hawking radiation seem broadly unconvincing compared to the Wilsonian renormalization-group universality arguments for condensed matter physics.Motivated by their apparent failure, compared with the overwhelming success of universality arguments in so many other contexts, I address the question: in which situations should we expect to be able to construct successful universality arguments? In other words, which situations are 'universality-argument-apt'? I distinguish between two notions of success for a universality argument: 'strength' and 'relevance'. I argue that we should only expect to be able to construct universality arguments that are successful in the sense of being significantly relevant to a given domain if 1 we know enough about how that domain's micro-physics is structured, or 2 we are able to empirically test the domain's macro-behaviour, or if we are in both situations at once. These conditions are useful, most obviously, as a clarification of what universality arguments are capable of. But I argue that they are also useful for two less direct reasons: they clarify the status of analogue experimentation, and thereby show us where we stand in our search for empirical confirmation of Hawking radiation.