Small transmitting loops can work fairly well above a few MHz, but they
are expensive to make. They need very low loss (because the radiation
resistance is almost nil) and a very high-voltage (10's of kV)
motor-driven capacitor arrangement. You can easily buy them
commercially covering 10 MHz - 30 MHz. They are an option if you don't
have space for a large antenna, don't mind shelling-out $380+ bucks,
and don't mind re-tuning whenever you change operating frequency.

I understand the H-fields are huge close-in, so one needs to be
careful.

73
-JJ