The localized surface plasmon resonance (LSPR) sensitivity of metal nanostructures is strongly dependent on the interaction between the supporting substrate and the metal nanostructure, which may cause a change in the local refractive index of the metal nanostructure. Among various techniques used for the development of LSPR chip preparation, solid-state dewetting of nanofilms offers fast and cost effective methods to fabricate large areas of nanostructures on a given substrate. Most of the previous studies have focused on the effect of the size, shape, and inter-particle distance of the metal nanostructures on the LSPR sensitivity. In this work, we reveal that the silicon-based supporting substrate influences the LSPR associated refractive index sensitivity of gold (Au) nanostructures designed for sensing applications. Specifically, we develop Au nanostructures on four different silicon-based ceramic substrates (Si, SiO2, Si3N4, SiC) by thermal dewetting process and demonstrate that the dielectric properties of these ceramic substrates play a key role in the LSPR-based refractive index (RI) sensitivity of the Au nanostructures. Among these Si-supported Au plasmonic refractive index (RI) sensors, the Au nanostructures on the SiC substrates display the highest average RI sensitivity of 247.80 nm/RIU, for hemispherical Au nanostructures of similar shapes and sizes. Apart from the significance of this work towards RI sensing applications, our results can be advantageous for a wide range of applications where sensitive plasmonic substrates need to be incorporated in silicon based optoelectronic devices.