The orbits of giant extrasolar planets often have surprisingly small semi-major axes, large eccentricities, or severe misalignments between their normals and their host stars spin axes. In some formation scenarios invoking Kozai-Lidov oscillations, an external planetary companion drives a planet onto an orbit having these properties. The mutual inclinations for Kozai-Lidov oscillations can be large and have not been confirmed observationally. Here we deduce that observed eccentric warm Jupiters with eccentric giant companions have mutual inclinations that oscillate between 35-65 deg. Our inference is based on the pairs observed apsidal separations, which cluster near 90 deg. The near-orthogonality of periapse directions is effected by the outer companions quadrupolar and octupolar potentials. These systems may be undergoing a stalled version of tidal migration that produces warm Jupiters over hot Jupiters, and provide evidence for a population of multi-planet systems that are not flat and have been sculpted by Kozai-Lidov oscillations.
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