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For Part 1 see ibid., vol.4, pp.67-70 (2003). In Part 1, closed-form formulas were proposed for basic parameters of coplanar-strip (CPS) waveguides on multilayer dielectric substrates. In Part 2, a new partial capacitance technique is proposed to deal with the case where the permittivity of the substrate layers increase away from the strips, and the magnetic wall approximation between the dielectric layers used in Part 1 is not valid. CPS on a SiO2/Si substrate is a typical example. Conformal mapping technique is also used for the evaluation of the line inductance (including internal) of the strips. The line capacitance, inductance, and conductance are then used to evaluate the frequency-dependent complex impedance, effective dielectric permittivity, and losses. The results are in good agreement with experiments and numerical simulations. The computation time is at least an order of magnitude shorter in comparison with the available commercial software (e.g., Momentum, Sonnet).