Global Climate Models (GCMs) are critical tools for understanding and projecting climate variability and change, yet the performance of these models is notoriously weak over much of tropical Africa. To improve this situation, process-based studies of African climate dynamics and their representation in GCMs are required. Here, we focus on summer rainfall of eastern Africa (SREA), which is crucial to the Ethiopian Highlands and feeds the flow of the Blue Nile River. The SREA region is highly vulnerable to droughts, with El Nino Southern Oscillation (ENSO) being a leading cause of interannual rainfall variability. Adequate understanding and accurate representation of climate features that influence regional variability is an important but often neglected issue when evaluating models. We perform a process-based evaluation of GCMs, focusing on the upper troposphere Tropical Easterly Jet (TEJ), which has been hypothesized to link ENSO to SREA. We find that most models have an ENSO-TEJ coupling similar to observed, but the models diverge in their representation of TEJ-SREA coupling. Differences in the latter explain the majority (80%) of variability in ENSO teleconnection simulation across the models. This is higher than the variance explained by rainfall coupling with the Somali jet (44%) and African Easterly Jet (55%). However, our diagnostics of the leading hypothesized mechanism in the models—variability in divergence in the TEJ exit region—are not consistent across models and suggest that a deeper understanding of the mechanisms of TEJ-precipitation coupling should be a priority for studies of climate variability and change in the region.