If I have pulsed dc current going though an electromagnet, with the magnetic field mimic the current at higher pulsed dc frequencies?
How are you going to produce Ghz current pulses into an INDUCTOR (For such an electromagnet is)? 

V=LdI/dt after all, so doing anything much to a significant inductance at Ghz rates implies a hell of a lot of voltage. 

Further at GHz rates the physical length of a conductor has to be small for it to appear as a lumped element, the wavelength at 1Ghz being only ~20cm in a typical copper wire after all, and you would need to keep things down to maybe 1/10th of a wavelength to make the usual low frequency approximations still work. If you want anything other then a sine wave, you need to do the sums to see what your physical dimension limit is for the highest harmonic of interest. 

Usually by the time we are looking at GHz rates, we are talking electromagnetic fields rather then electric or magnetic ones, physical size being less of an issue in the far field (Which is electromagnetic in nature).