This seems to be a way of improving the performance of analog high-frequency (GHz range) integrated circuits. Too bad that all the articles I found about this topic are behind a IEEE paywall. I think I could download them at my former University if there is interest in more details about this technique.
The basic bandwidth limitation of many circuits is the low pass RC filter formed by the resistance of the signal source (which may be a transmission line which "looks" like a resistance) and the input capacitance of an amplifier circuit.
By adding some inductance the input capacitance can be brought to resonance and "neutralized". If you choose the right inductance value you can place the resonant frequency (and the peak of the LC characteristic from which this technique takes its name) near the low pass frequency limit of the original circuit to boost the signal amplitude a little and therefore improve the bandwidth.
This isn't how the physics works, but from a circuit point of view you can think of a inductor as having current inertia. The bigger the inductor, the more inertia the current has.
When you apply a fixed voltage accross a inductor, the current builds up linearly. If you were then to short out the inductor so the current could circulate, it would do so forever if the inductor were perfect. Real inductors you can buy are made from wire, so have some finite resistance. The current times that resistance builds up a reverse voltage that slows down the current. But since the reverse push is proportional to the current, not fixed, the current decays exponentially instead of in a linear ramp if the current was fixed.
Actually inductors have been made from superconducting material, and they really do circulate current forever if the whole loop is superconducting.
If you can picture a inductor providing inertia to current and therefore how a fixed voltage causes the current to linearly ramp up, it's time to consider what happens when someone tries to suddenly interrupt that current. Think of trying to instantly stop a moving mass. Two things will happen. First, it won't stop instantly. Second the mass will create a great deal of force against whatever is trying to stop it. The inductor will do the same, but here force is voltage. The faster you try to stop the current, the more the inductor will push back with higher voltage.
But you say, a switch stops the current instantly when opened. Even if a switch were perfect and could do that, there would still be some point at which the contacts just barely separated. The inductor doesn't have to create much voltage for the current to arc between the contacts. Once a arc is formed, it's easier to keep it going at greater distances. That's because the air you see light up as a spark has become a plasma, which conducts electricity fairly well. So the switch contacts may have separated, but are now still connected by a plasma arc "wire". It does take some voltage to keep this arc going, which pushes backwards against the inductor current, which causes the current to decrease.
Eventually there won't be enough current to keep the arc going, and the switch is finally completely open. At that point most of the energy stored in the inductor has been spent, and the little that's left charges up the inevitable parasitic capacitance that always exists accross the inductor. Now you have a L-C tank circuit that will oscillate back and forth for a while. The little remaining energy is dissipated by the resistance of the wire in the inductor as the current sloshes back and forth thru it. The oscillations die down, and everything is finally truly off to the extent you can measure or care about.
This arcing accross switches is very real and a problem for switches and relays. This is one reasons relays wear out and often have different ratings for inductive loads. Every arc will damage the switch a little bit, which is considered in the lifetime cycles rating of the switch or relay.
Transistors can also be used to switch off inductors quickly. In fact, this is the basis for the common boost converter switching power supply topology. By charging up a inductor with current and then deliberately trying to switch it off quickly, you can harness the fact that the inductor will make a higher voltage for you than you started with.
Best Answer
You could resonate it with a parallel or series capacitor and use a signal generator and o-scope for finding the resonant-frequency. You need to have a capacitor of at least 50 times it's likely self capacitance but, that can also be measured with a frequency generator and an o-scope. Then add a known capacitor (say 10nF) and you should see the resonant frequency drop at least ten if not 100 times. Use this formula: -
\$f_R = \dfrac{1}{2 \pi \sqrt{LC}}\$
I regularly build coils for transmitting power from fixed units to rotating electronics and the parallel resonance way is the most reliable for accuracy.
You should also note that depending on the material of the ferrite the inductance may change quite significantly with current passed through it - this is due to the onset of saturation but some ferrites are designed to be like this so, if possible try and run the test with an oscillator delivering enough voltage to impart the right amount of current into the coil.