This paper is focused on the modeling and design of high-frequency planar coupled inductors with orthogonal air gaps. In coupled inductors, ac flux cancellation in part of the core segments results in reduced core losses and higher overall power density. However, with ac flux cancellation, fringing flux effects result in a more pronounced uneven current distribution compared to uncoupled inductors. A simple 1D analytical framework shows how the orthogonal air gaps can be utilized to minimize the ac winding resistance in coupled inductors. The proposed approach is verified using 2D and 3D finite-element simulations. System-level advantages of the proposed technique are compared for coupled inductors carrying dc currents with small ac ripple, and for coupled inductors with only ac current without any dc bias. Experimental results are presented for coupled inductors in two application examples: a two-phase boost converter, and a capacitively isolated transformerless stacked active bridge converter. While significant reductions in ac winding losses are obtained in both cases, the system-level impact is more significant in the case of coupled inductors carrying only ac currents.