Understanding the properties of electronic transport across metal-molecule interfaces is of central importance for controlling a large variety of molecular-based devices such as organic light emitting diodes, nanoscale organic spin-valves and single-molecule switches. One of the primary experimental methods to reveal the mechanisms behind electronic transport through metal-molecule interfaces is the study of conductance as a function of molecule length in molecular junctions. Previous studies focused on transport governed either by tunneling or hopping, both at low conductance. However, the upper limit of conductance across molecular junctions has not been explored, despite the great potential for efficient information transfer, charge injection and recombination processes. Here, we study the conductance properties of highly transmitting metal-molecule-metal interfaces, using a series of single-molecule junctions based on oligoacenes with increasing length. We find that the conductance saturates at an upper limit where it is independent of molecule length. Furthermore, we show that this upper limit can be controlled by the character of the orbital hybridization at the metal-molecule interface. Using two prototype systems, in which the molecules are contacted by either Ag or Pt electrodes, we reveal two different origins for the saturation of conductance. In the case of Ag-based molecular junctions, the conductance saturation is ascribed to a competition between energy level alignment and level broadening, while in the case of Pt-based junctions, the saturation is attributed to a band-like transport. The results are explained by an intuitive model, backed by ab-initio transport calculations. Our findings shed light on the mechanisms that constrain the conductance at the high transmission limit, providing guiding principles for the design of highly conductive metal-molecule interfaces.