Density functional theory calculations have been performed to provide mechanistic insight into a series of Cp∗CoIII- and Cp∗RhIII-catalyzed directed C-H bond functionalizations with diazo-compound substrates. Co-based catalysis proceeds through five steps: C-H bond activation; C-C coupling via a concerted 1,2-aryl transfer; proto-demetalation; nucleophilic addition; and solvent-assisted methanol elimination. C-H bond activation is predicted to be reversible, consistent with deuterium-scrambling experiments. The higher Lewis acidity of Co compared to Rh for two otherwise identical catalysts increases the susceptibility of a coordinated carbonyl group to nucleophilic addition in the former, facilitating the formation of cyclized products not observed for Rh. Methanol elimination is predicted to be the turnover-limiting step for one substrate, and this is facilitated by solvent 2,2,2-trifluoroethanol (TFE) acting as a proton shuttle. Theory suggests that further tuning of acidity may offer opportunities for improving catalysis. We also assess the role of a pyridine group that leads to a different series of final steps in one Rh-based catalytic cycle, thereby enabling access to the otherwise suppressed cyclization product. Our study of an alternative Rh-based system having acetate ligands replaced with MeCN indicates that C-H bond activation is sensitive to those ligands and variation can affect which step is turnover-limiting.