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In this paper, a new realization of left-handed transmission lines (LHTLs) is presented. The proposed structure employs a coaxial waveguide structure to host periodic arrays of split-ring resonators (SRRs) and capacitively loaded strips (CLSs). The SRRs and CLSs are radially mounted on the inner conductor of the coaxial waveguide structure, which provides the necessary polarization for the periodic arrays of SRRs and CLSs to exhibit a negative index of refraction over a specific frequency band. The structure of the proposed coaxial waveguide-based LHTL (CW-LHTL) is optimized by studying the effect of inductive and capacitive couplings on the performance of the structure. The properties of CW-LHTL are studied by analyzing the dispersion diagram and extracting its effective permittivity and permeability. The analysis shows that the proposed CW-LHTL exhibits negative effective permittivity and permeability around the resonant frequency of the SRRs. The inductive and capacitive couplings of the SRRs and CLSs of a CW-LHTL unit cell are related to the periodicity of left-handed material (LHM) in free space. Therefore, the proposed CW-LHTL provides a reliable measurement setup to study the behavior of LHM in free space without the need to use a large number of unit cells. The coaxial waveguide measurement setup is also used to analyze different modified SRRs, which have a smaller size while operating at the same resonant frequency. A coaxial waveguide structure housing a unit cell of the proposed SRR is fabricated and tested. The measurement results show that the proposed modified SRR is up to 46% smaller in size in comparison with the traditional SRR. The applications of CW-LHTL in guided microwave systems are also discussed.