In this paper, new and fast analytical formulations have been presented for conductor loss calculations of elliptical (ECPW) and cylindrical coplanar waveguide (CCPW) with finite conductor thickness. These expressions are derived using conformal mapping techniques (CMT) and the validity of them is established by comparing the numerical results in the literature. These comparisons indicate that for the same conductor thickness the conductor losses of elliptical and cylindrical coplanar waveguide are higher than the conductor losses of coplanar waveguide presented in (1). Calculation method developed in this study is an extension of the approximate technique proposed by Ghione (1).