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Gold nanoantennas have been used in a variety of biomedical applications due to their attractive electronic and optical properties, which are shape- and size-dependent. Here, a periodic paired gold nanostructure exploiting surface plasmon resonance is proposed, which shows promising results for Refractive Index (RI) detection due to its high electric field confinement and diffraction limit. Here, single and paired gold nanostructured sensors were designed for real-time RI detection. The Full-Width at Half-Maximum (FWHM) and Figure-Of-Merit (FOM) were also calculated, which relate the sensitivity to the sharpness of the peak. The effect of different possible structural shapes and dimensions were studied to optimise the sensitivity response of nanosensing structures and identify an optimised elliptical nanoantenna with the major axis a, minor axis b, gap between the pair g, and heights h being 100 nm, 10 nm, 10 nm, and 40 nm, respectively. In this work, we investigated the bulk sensitivity, which is the spectral shift per refractive index unit due to the change in the surrounding material, and this value was calculated as 526–530 nm/RIU, while the FWHM was calculated around 110 nm with a FOM of 8.1. On the other hand, the surface sensing was related to the spectral shift due to the refractive index variation of the surface layer near the paired nanoantenna surface, and this value for the same antenna pair was calculated as 250 nm/RIU for a surface layer thickness of 4.5 nm.