Light extraction from organic light-emitting diodes that utilize phosphorescent materials has an internal efficiency of 100% but is limited by an external quantum efficiency (EQE) of 30%. In this study, extremely high-efficiency organic light emitting diodes (OLEDs) with an EQE of greater than 50% and low roll-off were produced by inserting a vacuum nanohole array (VNHA) into phosphorescent OLEDs (PhOLEDs). The resultant extraction enhancement was quantified in terms of EQE by comparing experimentally measured results with those produced from optical modeling analysis, which assumes the near-perfect electric characteristics of the device. A comparison of the experimental data and optical modeling results indicated that the VNHA extracts the entire waveguide loss into the air. The EQE obtained in this study is the highest value obtained to date for bottom-emitting OLEDs.