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The paper proposes the use of a coaxial waveguide structure to realize a left-handed transmission line (LH-TL) structure. The structure consists of periodic arrays of split-ring resonators (SRRs) and capacitively loaded strips (CLSs) mounted radially on the inner conductor. The coaxial waveguide structure provides a suitable guided environment to measure the characteristics of negative index materials (NIMs). The paper also presents a modified SRR structure that offers more than 45% size reduction in comparison with the traditional SRR. A coaxial waveguide structure housing a unit-cell of the proposed SRR is fabricated and tested. The experimental results confirm the validity of the proposed concept.