This work introduces a refined technique for the estimation of films permittivity within the Ka-band using free-space measurement method. Addressing the challenge of wrong solutions in permittivity estimation, our approach incorporates a frequency-dependent objective function, to find a unique estimation solution. We apply this technique to a variety of thin and flexible substrates, including cycloolefin polymer (COP), polyethylene terephthalate (PET), and polyimide (PI) films, and quantitatively analyze the uncertainty on the estimated permittivity and loss tangent. The proposed technique can offer a method for determining the permittivity of not only thin media but also flexible printed circuit boards used for circuits and antennas.