We present an electrical and optical model for simulating the current distribution in and the resonant light emission from nanostructured organic light-emitting diodes (OLEDs). A periodic nanostructure in an OLED can be used as a resonant waveguide grating to tailor the light emission, i.e., to direct the dominant emission wavelength into a specific direction. We show that the current injection at nanostructured electrodes is strongly enhanced at their corners, leading to localized current paths and emission zones. These current paths have to be overlapping with the resonant optical field hot spots in order to gain maximal resonant light outcoupling. We show that this is not generally the case for periodically nanostructured OLEDs and that the introduction of local isolation layers can improve the overlap by altering the current paths. Depending on the isolation layer configuration either the resonant or non-resonant light outcoupling is pronounced. This optimization potential may be beneficial for compact organic optoelectronic sensors that require highly directional OLED emission.