Metallic nanoparticles play an important role in the design of sensing platforms. In this paper, a new electromagnetic study for conical metal nanoparticles, working in the Near Infrared and Visible frequency regime, is proposed. The structures consist of inclusions, arranged in an array configuration, embedded in a dielectric environment. The aim of this work is to develop new analytical models, in order to describe the nanoparticles electromagnetic behavior in terms of extinction cross-section (absorption and scattering). The closed-form formulas link the conical nanoparticles geometrical and electromagnetic parameters to their resonant frequency properties in terms of wavelength position, magnitude and bandwidth. The proposed models are compared to the numerical results and to the experimental ones, reported in literature. Good agreement is obtained. The proposed analytical formulas represent useful tools for sensing applications. For this reason, exploiting such models a new sensing platform able to detect different blood diseases is obtained. Numerical results confirm the capability of the proposed structure to be used as a sensing platform for medical diagnostics.