Does my EM signal have to match the intrinsic impedance of free space to travel?

If I have a resonating LC circuit that is tuned to 50 Ohms using an antenna tuner (because my amplifier's output is designed for 50 ohm output), the L is producing an alternating magnetic field and the two reactive components are exchanging reactive power back and forth. But in this case my L is also an antenna (in my wireless power transfer experiment) and I was wondering if my setup will radiate any power in the far field because the H field is much larger than the E field so the ratio is not 377 ohms. Is this correct? But the antenna is matched for 50 ohms so it can radiate. It's weird because its 2 differents things: matching the antenna to your power amplifier, and matching your antenna to free space. I've matched my antenna to my signal source for 50 ohms, but my transmitter is just a large coil which is producing large alternating magnetic field which technically the ratio is no longer 377 so it will not radiate? I don't want my L to radiate power in the far field, I just want to keep the power in the near field. I'm operating at 2 MHz.