What you seem to be referring to (a guess from your mention of quantum tunneling) is perhaps near-field magnetic induction.
Here's a summary - magnetic coils have a near-field region around them, the primary contriubtion to which involves minimal radiation of power. This region is dominated by the response of the coils (for example) to the fields, and is therefore a kind of evanescent wave (i.e. something that is present around a source only for a small distance).
On the other hand, we have the usual resonant inductive coupling, where two coils have the same natural frequency, and this maximizes the transfer of energy between them. The reason it is a maximum here is because when they have different natural frequencies, there are times when the natural restoring 'force' is out of phase (i.e. pulling oppositely) with the external 'force', effectively cancelling each other out. A simple (i.e. driven harmonic oscillator) treatment of this may be found here. It obviously still obeys the conservation of energy, and cannot transfer unreasonably large amounts of energy without limits. It's just that it is much more efficient that not having resonance.
When you combine the two, you simply have resonant coupling within the near-field regions. This is a good way to maximize the transfer of energy, simply because the near-field region is where the field is still fairly strong, and resonance is where maximum energy transfer occurs.
This obviously can't be used for energy transfer over very large distances; it's only that you can make the near-field region large enough for practical purposes. This is seemingly being implemented by some company.
Quantum tunneling occurs from a similar kind of "evanescent wave". Consider a particle in a finite potential well: while the solutions for the wavefunction are sinusoidal oscillations within the well, they decay rapidly with distance into the walls. However, when the wall is very thin, the wavefunction is still large enough at the other end, leading to a significant probability of finding the particle on the other side of the wall, even though it does not classically have the energy to cross the wall (see, for example, this picture). This has similarities with the "near-field" part (in the wall region), but not with the "resonance" part.