Air gap variation between metal target and planar Inductor coil changes the coil inductance and oscillating signal's frequency & amplitude?
The inductance is reduced by proximity to conductive metal. Effectively the metal acts as a shorted turn. 

The Q is also reduced because the inductance goes down but the series resistance of the coil remains the same. 

For a given voltage the current will go up because of the shorted turn effect. So it depends on the oscillator circuit and whether there is some form of AGC (automatic gain control) and what the limits are on output drive  power/current.