In this paper, the accuracy of the singularity expansion method (SEM) used for antenna characterization is investigated. A well-known limitation of the SEM is that pole extraction is very sensitive to noise. A comparison between two main methods of pole extraction is presented. The matrix pencil (MP) method and the Cauchy's method are used to extract poles from the radiated fields of a dipole antenna and two bowtie antennas. Results are presented for simulated fields, and the robustness to a white Gaussian noise is also analyzed. We show that the MP method allows working with lower SNR than Cauchy's method and is more accurate for field reconstruction.