In this paper, a predictive electrical model of the slow-wave coplanar waveguide structure (S-CPW) is presented. The model was developed under the assumption of Quasi-TEM propagation mode. This assumption allows treating separately the electric field from the magnetic field. Therefore, inductive and capacitive effects are processed apart. Within this context, analytical formulas, parameterized by S-CPW geometric dimensions, are given for each electric parameter in the model, including resistances that account for losses. The model was validated with electromagnetic simulations (HFSSTM) and measurement results on several integrated technologies. An excellent agreement was achieved over a wide frequency band from DC up to 110 GHz, with a maximum error of 10%. Consequently, the model provides a fast and powerful tool for designing circuits based on S-CPW. The developed model enables a better insight of how geometries influence the overall S-CPW performance. The model was applied to the design of a quarter-wave length transmission lines and tunable phase shifter. The transmission lines were optimized in terms of performance, minimum length or surface. The tunable phase shifter was designed by embedding varactors in the S-CPW floating shield. These designs highlight the efficiency of the model for complex optimization or complex circuits design, respectively.