How can I determine the signal level needed into a given antenna to produce a given magnetic field at a given distance?
If you already have the electric fieldstrength, the rest is easy. The ratio of the electric and magnetic fieldstrength is called the impedance of free space its value is approximately 377 ohms.

So approximately: $$H = { E \over 377 } $$
H and E are the moduli of the respective field vectors.