Ultrasound shear wave elastography (SWE) methods are being used to differentiate healthy versus diseased tissue on the basis of their viscoelastic mechanical properties. Tissue viscoelasticity is often studied by analyzing shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. Recently, a unique approach using a generalized Stockwell transformation (GST-SFK) was proposed for the calculation of dispersion curves in viscoelastic media over expanded frequency band. In this work, the method’s robustness was evaluated on data from five custom-made viscoelastic tissue-mimicking phantoms and sixty in vivo renal transplants. For each phantom, 15 shear wave motion data acquisitions were taken, while 10–13 acquisitions were acquired for renal transplants measured in the renal cortex. For each data-set mean and standard deviation (SD) of estimated phase velocity dispersion curves were studied. In addition, the viscoelastic parameters of the Zener model were examined, which were preceded by a convergence analysis. For viscoelastic phantoms scanned with a research ultrasound scanner, and for the in vivo renal transplants scanned with a clinical scanner, the decisive advantage of the GST-SFK method over the standard two-dimensional Fourier transform (2D-FT) method was shown. The GST-SFK method provided dispersion curve estimates with lower SD over a wider frequency band in comparison to the 2D-FT method. These advantages are relevant to the analysis of the mechanical properties of tissues in clinical practice to discriminate healthy from diseased tissue.