The *most accurate* way of solving this problem is to use the HFSS-IE solver in conjunction with the FEM solver to perfectly truncate the air region surrounding your antenna. This is the so-called FEBI method (Finite Element-Boundary Integral). Using the IE solver to truncate the region affords the most accuracy with the smallest air region. The mechanics of this are to simply assign the Radiation BC to the airbox, and then enable the option to "Model Exterior as HFSS-IE domain."
I would also recommend against using the Fast Frequency Sweep for these broadband antennas. An Interpolating sweep for the S-parameters is best, and then a Discrete sweep for the individual points where you need fields is usually sufficient. There is also a new option in the Discrete sweep to save only radiating fields. This can help conserve disk space for large problems.