Western boundary currents-such as the Agulhas Current in the Indian Ocean-carry heat poleward, moderating Earth's climate and fuelling the mid-latitude storm tracks. They could exacerbate or mitigate warming and extreme weather events in the future, depending on their response to anthropogenic climate change. Climate models show an ongoing poleward expansion and intensification of the global wind systems, most robustly in the Southern Hemisphere, and linear dynamical theory suggests that western boundary currents will intensify and shift poleward as a result. Observational evidence of such changes comes from accelerated warming and air-sea heat flux rates within all western boundary currents, which are two or three times faster than global mean rates. Here we show that, despite these expectations, the Agulhas Current has not intensified since the early 1990s. Instead, we find that it has broadened as a result of more eddy activity. Recent analyses of other western boundary currents-the Kuroshio and East Australia currents-hint at similar trends. These results indicate that intensifying winds may be increasing the eddy kinetic energy of boundary currents, rather than their mean flow. This could act to decrease poleward heat transport and increase cross-frontal exchange of nutrients and pollutants between the coastal ocean and the deep ocean. Sustained in situ measurements are needed to properly understand the role of these current systems in a changing climate.