Polarimetric Phased Array Radar (PAR) technology is being considered for next-generation meteorological observations supporting research and operations. One of the most important PAR capabilities for high temporal resolution observations is the beam broadening on transmission ("spoiled beam") and simultaneous reception through digital beamforming. In this paper, we present a polarimetric antenna pattern synthesis method that considers distinct antenna element patterns radiated in the horizontal (H) and vertical (V) polarizations. The mismatch in element-level H/V copolar antenna patterns has a direct impact on the farfield transmit beams that can bias polarimetric weather measurements. The synthesis optimization searches for independent sets of phase-only element excitations for the H and V polarizations, such that farfield intentionally broadened antenna patterns are matched. Preliminary results show that mismatches integrated over the transmit beam mainlobe can be reduced from approximately 1.87 dB to 0.28 dB at broadside. Simulation results indicate that improving H/V beam matching mitigates biases in the copolar correlation coefficient.