The following application note suggests the possibility of doing what you want to do without the necessity of building RF type circuits which can be a challenge for experimenting.

https://www.analog.com/en/design-notes/wireless-li-ion-charger-solution-for-wearable-devices.html

The application note describes a VCO (Voltage Controlled Oscillator) that excites an LC tank circuit that can transfer power across a small air gap. Here is a simulation of that circuit using ideal components. Using real components will probably not be quite as good, but it seems like 50% might be achievable.

 

Are you saying you have a device that charges wirelessly at 13.56 MHz? If so, please link us to the specifications.

I am skeptical, wireless phone chargers charge at around 100 KHz, I would be surprised if both frequencies are equally usable.

Unless maybe you are talking about hearing aids, the small size might dictate the higher frequency.