An analytical formulation for relative dielectric constant retrieval is reconstructed to establish a relationship between the response of a spiral microstrip resonator and effective relative dielectric constant of a lossy superstrate, such as biological tissue. To do so, an analytical equation is modified by constructing functions for the two unknowns, the filling factor A and effective length l(eff) of the resonator. This is done by simulating the resonator with digital phantoms of varying permittivity. The values of A and l(eff) are determined for each phantom from the resulting S-parameter response, using particle swarm optimization. Multiple nonlinear regression is applied to produce equations for A and l(eff), expressed as a function of frequency and the phantom's relative dielectric constant. These equations are combined to form a new nonlinear analytical equation, which is then solved using the Newton-Raphson iterative method, for both simulations and measurements of physical phantoms. To verify the reconstructed dielectric constant, the dielectric properties of the physical phantoms are determined with commercial high temperature open-ended coaxial probe. The dielectric properties are reconstructed by the described method, with less than 3.67% error with respect to the measurements.