In this work, we have applied a moment-method-based simulation code to perform a detailed parametric study of the bandwidth, cross-polarization level, and the feed location characteristics of the matched Hilbert antenna. It is shown that a properly chosen off-center near-the-end feed point may provide an approximate 50-Ω real input impedance at the fundamental resonant frequency. The role of different iteration order for Hilbert antennas, approximately matched to 50-Ω line, on the bandwidth and cross-polarization level of such antennas are investigated numerically. As was shown by Vinoy et al. the radiation patterns resemble those of a linear dipole and for a fixed-area-matched Hilbert antenna, the resonant frequency can be lowered by increasing the iteration order n. However, for such matched antennas, the bandwidth for VSWR < 2 will be decreased and the cross-polarization level may be different for the higher iteration-order antennas.