The interaction between electromagnetic waves and materials is related to dielectric properties of materials, which have been used for technological applications in many fields, like polymers. Extracting complex permittivity values can be used to define the materials by using a specific wavelength in the fields of communication, optics or high-frequency electronics. This paper summarizes obtaining complex permittivity of materials by using free space measurement methods. A non-destructive/non-contactless measurement method was used to obtain S-parameters using a vector network analyzer. The Gaussian process regression (GPR) method, which is an artificial intelligence (AI) tool, is proposed as an alternative to numerical and analytical calculation methods to obtain complex permittivity value, and the results were confirmed by the Newton-Raphson method. GPR results were obtained to be more accurate than that of well-known methods and other alternative AI methods. In previous studies, complex permittivity has been extracted by using imaginary and real parts of the data together. Instead, with GPR, either the real and imaginative part of the S21 parameters can be used together or the real and imaginary parts of the complex permittivity can be estimated separately, depending on the input values of the proposed estimation method.