Hummingbirds and nectar bats are the only vertebrates that are specialized for hovering in front of flowers to forage nectar. How their aerodynamic performance compares is, however, unclear. To hover, hummingbirds consistently generate about a quarter of the vertical aerodynamic force required to support their body weight during the upstroke. In contrast, generalist birds in slow hovering flight generate little upstroke weight support. We report that nectar bats also generate elevated weight support during the upstroke compared to generalist bats. Comparing 20 Neotropical species, we show how nectarivorous birds and bats converged on this ability by inverting their respective feathered and membrane wings more than species with other diets. However, while hummingbirds converged on an efficient horizontal wingbeat to mostly generate lift, bats rely on lift and drag during the downstroke to fully support their body weight. Furthermore, whereas the ability of nectar bats to aerodynamically support their body weight during the upstroke is elevated, it is much smaller than that of hummingbirds. Bats compensate by generating more aerodynamic weight support during their extended downstroke. Although, in principle, it requires more aerodynamic power to hover using this method, bats have adapted by evolving much larger wings for their body weight. Therefore, the net aerodynamic induced power required to hover is similar among hummingbirds and bats per unit body mass. This mechanistic insight into how feathered wings and membrane wings ultimately require similar aerodynamic power to hover may inform analogous design trade-offs in aerial robots.