High Q-factor bandstop filter based on broadside-coupling between U-shaped coplanar waveguide (CPW) resonator and CPW through-line (CPWTL) is proposed in the present paper. The CPWTL is printed on the top layer of the dielectric substrate whereas the CPW resonator (CPWR) is printed on the bottom layer. Only over very narrow frequency band around the resonant frequency of the CPWR the microwave power flowing in the CPWTL is coupled to (absorbed by) the CPWR leading to a bandstop filter of very high Q-factor. A CPWR with side ground strips of finite width is shown to have much higher Q-factor than that of infinitely extending side ground planes. Owing to the lower profile of the CPW with finite-width, the radiation loss is reduced, and the structure has narrower frequency band for coupling, which results in much higher Q-factor than other published works. The dimensions of the CPWTL are optimized for impedance matching whereas the dimensions of the Ushaped CPWR are optimized to obtain the highest possible Q-factor. The effect of the loss tangent of the dielectric substrate material on the Q-factor is investigated. A prototype of the proposed filter is fabricated and experimentally studied for more understanding of the underlying physical principles of operation and for experimental investigation of the filter performance. The experimental measurements show good agreement with the corresponding simulation results.