I'm trying to understand the behaviour of electromagnetic coupling between two coils. One of my coils is connected to the output of a Colpitts oscillator as shown below with the excited coil labelled as L1 and I want to observe the voltage and frequency characteristics of another coil when placed directly on top of the excited one. I'm pretty sure I can't just have the disturbed coil floating. My thoughts is to have impedance matching on the disturbed coil where one part of the coil is connect to common ground used in the oscillator circuit which then connects to a load and then back to ground again. Is this design satisfactory or am I missing something?
Despite the title, it seems you are really only asking about magnetic coupling.
Basically, you want the two coils to work like a transformer. That could be doable, depending on how much the magnetic field extends outside the physical volume of these coils. If these are "shielded" inductors, for example, then they are deliberately designed to contain most of the magnetic field inside. Two such devices would work poorly as a transformer.
If you really want to transfer power from one coil to another, then get a transformer or make one yourself. These have both coils wound around the same magnetic core. Ideally, the magnetic fields of both coils overlap completely.
As for what to do with the second coil, consider it the secondary of a transformer, since it is. Its common mode voltage can float with respect to your ground. This is only limited by the insulation between the coils. The circuit connected to the secondary can be completely isolated from your ground. For example, you can connect a battery-operated voltmeter across the secondary to measure the open-circuit AC voltage.