Transmit 12v power wirelessly
A few watts of power can be magnetically transferred a few inches using resonating coils. Not hard to do but if you expect a compact solution that is inexpensive you will be disappointed.

It works on the same principle as commonly used RFID readers: -



It's simpler of course because only power is transmitted and there is no need for data systems at either end. If you need to transmit a lot more power at a greater distance then sturdier coils are needed that have sub-milli-ohm losses: -



The basic principle is that a parallel resonant circuit (with extremely low losses), when driven with an alternating supply at the resonant frequency, will circulate several amps to many tens (or even hundreds) of amps between coil and tuning capacitor, This is the power transmit end.

The receiving end has the same arrangement i.e. it is tuned to match the resonant frequency and, even though it might only receive a small fraction of the magnetic flux produced, the resonance of the receive coil can still produce a substantial voltage that is enough to drive real power (watts to tens of watts) into a load: -