Changes in speciation and extinction rates are key to the dynamics of clade diversification, but attempts to infer them from phylogenies of extant species face challenges. Methods capable of synthesizing information from extant and fossil species have yielded novel insights into diversification rate variation through time, but little is known about their behavior when analyzing entirely extinct clades. Here, we use empirical and simulated data to assess how two popular methods, PyRate and Fossil BAMM, perform in this setting. We inferred the first tip-dated trees for ornithischian dinosaurs, and combined them with fossil occurrence data to test whether the clade underwent an end-Cretaceous decline. We then simulated phylogenies and fossil records under empirical constraints to determine whether macroevolutionary and preservation rates can be teased apart under paleobiologically realistic conditions. We obtained discordant inferences about ornithischian macroevolution including a long-term speciation rate decline (BAMM), mostly flat rates with (PyRate) or without (BAMM) a steep diversification drop, and episodes of implausibly accelerated speciation and extinction (PyRate). Simulations revealed little to no conflation between speciation and preservation, but yielded spuriously correlated speciation and extinction estimates while time-smearing tree-wide shifts (BAMM) or overestimating their number (PyRate). Our results indicate that the small phylogenetic datasets available to vertebrate paleontologists and the assumptions made by current model-based methods combine to hinder inferences about the diversification of extinct clades. We provide guidelines for interpreting the results of the existing approaches in light of their limitations, and suggest how the latter may be mitigated.