Phase transition that occurs around the spectral position of localized surface plasmon resonance (LSPR) has various applications for light manipulation and refractive index sensing. Previous studies focused on phase responses of specific plasmonic structures, whereas the general theoretical analysis remains inadequate. In this study, we analytically modeled the phase spectra and the intensity spectra of silver nanodots with temporal coupled-mode theory. The phase transition occurs at the transmission dip, whereas the phase of reflection varies much more gradually. We further derived the equation for the slope of the phase at the transmission dip, which is a function of the rates of Ohmic dissipation and emission. The theoretical analysis is also applicable for wide varieties of LSPR systems and provides an intuitive physical mechanism for phase properties. Then, based on the fundamental discussion, we further investigated plasmonic phase retardation in anisotropic nanodots for the application of boosting the figure of merit (FOM) of refractive index sensing. The anisotropic nanodots induce plasmonic phase transitions, which spectrally split, for transmission waves polarized along the symmetric axes. Thus, anisotropy induces relative phase retardation in the narrow spectral region between the wavelengths of the LSPRs. We numerically manipulated the full width at half maximum of the ellipsometric spectra by adjusting the aspect ratio of the nanodots and observed an FOM of 24.3. In addition, experiments were performed to demonstrate the feasibility of this arrangement.