A Heston model calibration technique is presented for European options under the Heston model. The novel Shannon Wavelets Inverse Fourier Technique (SWIFT) is extended for European option price calibration (previously it was used only for pricing European, Asian, barrier, and Bermudan options). This method has different expressions and speed-up techniques, adequate to different set-ups. These are discussed and new expressions and properties are presented for the gradient computation and option calibration. The Heston characteristic function expression recently proposed by \cite{cui17} is used in the SWIFT implementation due to its analytic gradient and its continuity properties. The time performance, robustness, and convergence under set-ups representative of real markets is studied for different implementations of the SWIFT technique and compared with the option calibration scheme presented by \cite{cui17} The SWIFT implementations are coded in C++ and uploaded to a public GitHub repository. The libray implements several of the different SWIFT expressions for GBM and Heston European options
