Single-molecule conductance studies on metal-containing inorganic and organometallic molecular wires are relatively less explored compared to those on organic molecular wires. Furthermore, conductance and transmission profiles of the metal-containing wires insensitive to the metal centers often hinder rational design for high performance wires. Here, synthesis and single-molecule conductance measurements of the bis(butadiynyl)rhodium wires with tetracarbene ligands 1(H) and 1(Au) are reported as rare examples for Rh(III) diacetylide molecular wires. The rhodium wires derived from the terminal acetylene and gold-functionalized precursors show comparable, high single-molecule conductance ((6-7) x 10(-3)G(0)) as determined by the STM break-junction measurements, suggesting formation of virtually the same covalently linked metal electrode-molecule-metal electrode junctions. The values for the metallapolyynes are larger than those of the organic polyyne wires having the similar molecular lengths. The hybrid DFT-NEGF calculations of the model systems suggest that profiles of transmission spectra are highly sensitive to the presence and species of the metal fragments doped into the polyyne molecular wire because the conductance orbitals of the metallapolyynes molecular junctions carry significant metal fragment characters. Thus, the metallapolyyne junctions turn out to be suitable platforms for rationally designed molecular wires.