Shear wave (SW) elastography is an ultrasound imaging modality that provides quantitative viscoelastic measurements of tissue. The phase difference method allows for local estimation of viscoelasticity by computing the dispersion curve using phases from two laterally-spaced pixels. However, this method is sensitive to measurement noise in the estimated SW particle velocities. Hence, we propose the delayed matrix pencil method to investigate this problem, and validated its feasibility both in-silico and in-vitro. The performance was compared with the original phase difference method and other two alternative techniques based on lowpass filtering and discrete wavelet transform denoising. The estimated viscoelastic values are summarized in box plots and followed by statistical analysis. Results from both studies show the proposed method to be more robust to noise with the smallest interquartile range in both elasticity and viscosity.