Hello,
Using a directional antenna reduces influence of reflections. As elchiquito says, a horn can be used. You should be able to rotate the antenna to produce vertical and horizontal polarization.
If its gain is known (for example horn), you can use the friis formula for determining the gain (of course make sure you are in the far field region for both antennas and make corrections for cable loss, etc). When the gain is not known, then exchange the DUT for a good constructed dipole with balun (Gi = 1.64 without correction for cable and balun loss), or other known antenna. Based on the difference in output from DUT and dipole, you can determine the gain for each linear polarisation.
Your antenna will produce more or less circular polarisation. You need to sum the gains for both horizontal and vertical orientation to find the total gain (not using dB's). If you want to know how well the field is circular polarised, you need to rotate the horn (or other antenna) to find the axial ratio.
You may know that you can interchange receiver and transmitter, whatever is convenient for you.