In this paper, a conductor-backed coplanar waveguide with sine edges (CBCPW-SE), consisting of a conductor-backed coplanar with periodic sine edges supported by a dielectric substrate, is proposed as a promising new transmission line (TL) at millimeter-wave and terahertz frequencies. This configuration offers a distinct advantage by maintaining a constant input impedance of 50 Ω across a broad frequency spectrum, eliminating the necessity for any additional impedance matching transitions, thereby enhancing the overall efficiency and simplicity of the transmission system. To verify the design, the CBCPW-SE was fabricated and measured. The measurement results demonstrate that, from 10 MHz to 100 GHz, the insertion loss is less than 0.1 dB/mm and the reflection coefficient is better than −10 dB. The measured S21 (dB) for a 50 mm-long CBCPW-SE section is less than −5 dB from 10 MHz to 100 GHz. The measured group delay per unit length of the trace is 3.4–5 ps, ranging from 10 MHz to 100 GHz. Moreover, the measured group velocity dispersion (GVD) approaches zero, signifying the minimal temporal spreading of the signal components, a crucial aspect for maintaining signal integrity and facilitating high-speed data transmission.