Just an idea:
As the reflection in a perfect conductive plane changes the hand of an eliptical polarization, I think you can perform this test:
a) Point the antennas directly and measure s21a.
b) Point the antennas through a perfect reflecting plane and measure s21b.
One of the measurements gives a value higher than the other (which one depends on whether the antennas are of the same or opposite hand).
|s21a| and |s21b| should be sufficient for calculate the axial ratio.
Notes:
The path length must be the same in both measurements
The direct path in b) must be highly attenuated (keep the antennas away, eventually use absorbers, etc.)
Reflected paths in a) must be highly attenuated
The plane must be "big" (ideally infinite)
The antennas should be in far field
The reflection angle is not of main importance
It is supposed that the reference antenna has axial ratio 1
Regards
Z