The conductance of a family of ruthenium-octene-ruthenium molecular junctions with different πconjugation are investigated using a fully self-consistent ab initio approach which combines thenonequilibrium Green's function formalism with density functional theory. Our calculationsdemonstrate that the continuity of the π conjugation in the contact region as well as along themolecular backbone affects the junction conductance significantly, showing the advantage of usingthe ruthenium-carbon double bond as the linkage of conjugated organic molecules.