Dear lord, what are you doing at 1GHz that needs a current probe? You're just doing a half-assed power tap or directional coupler (without the direction) -- these items being preferable as the impedance is controlled, so you don't introduce reflections.
Indeed, burden impedance is nowhere more significant than at high frequencies! You also have the problem of common mode impedance, which can be conveniently neglected at low frequencies, but is just as critical up there. This severely limits the extent to which you can even say you're measuring a current -- sure, you measured a signal across a resistance, but was that signal induced by electric or magnetic field?
And absolutely, there are instruments which can deal with these challenges -- but it sounds very much like an X-Y problem: you have problem X, and suspect you need a solution Y which you are asking us about; but you should really be asking us about X in the first place!
Musing:
The most extreme current probe I know of is the bunching detector in a particle accelerator. This is a length of beamline (metal pipe what the particle beam zips around inside of) that has been sectioned, so that as a bunch of particles passes, the moving field of that packet of charge (in other words, a current!) induces a voltage across the ends of the sectioned pipe. The impedance is controlled by way of beamline characteristics (it's a circular waveguide) and the exact shape of the section (usually, it's made such that the pipe diameter makes a step increase, and a magnetic core is placed in the resulting annulus), and the signal is taken out by simply tying off coax cables across the section. The cables must be evenly spaced (equal angles around the section), so that there isn't a tangential reflection. Only a 1:1 ratio is possible (or N:1 for N cables in parallel, really), and the pulses are very short indeed (a 1mm long particle bunch, travelling at the speed of light, emits a cone of current only 3.3ps long -- because of the physics of acceleration, the particles are pushed tighter together into groups -- bunches -- that can be quite short, and therefore the sense pulse is quite short indeed).
Tim