Sinuous antennas are capable of producing ultra-wideband radiation with polarization diversity. Such a capability makes the sinuous antenna an attractive candidate for wideband polarimetric radar applications. Additionally, the ability of the sinuous antenna to be implemented as a planar structure makes it a good fit for close in sensing applications such as ground penetrating radar. However, recent literature has shown the sinuous antenna to suffer from resonances which degrade performance. Such resonances produce late time ringing which is particularly troubling for pulsed close in sensing applications. The resonances occur in two forms: log-periodic resonances on the arms, and a resonance due to the outer truncation of the sinuous antenna geometry. A detailed investigation as to the correlation between the log-periodic resonances and the sinuous antenna design parameters indicates the resonances may be mitigated by selecting appropriate parameters. In addition, the resonance due to truncation may be mitigated by moving the circular truncation to the tip of the outermost cell which has advantages over the clipping method proposed in the literature.