Recent studies On hypervelocity stars (HVSs) have generated a need to understand the high velocity limits of binary systems. If runaway binary systems with high movement speeds well in excess of 200 km s(-1) were to exist, it would have implications on how HVS candidates are selected, and our current understanding of how they form needs to be reinforced. :In this paper, we explore the possibility that such high-velocity runaway binaries (HVRBs) can be engendered by supernova explosions of the tertiary in close hierarchical triple systems. We find that such explosions can lead to significant remnant binary velocities, and demonstrate via constraining the velocity distribution of such HVRBs that this mechanism can lead to binaries with centre-of-mass velocities of 350 km s(-1) or more, relative to the original centre of mass of the progenitor triple system. This translates into potential observations of binaries with velocities high enough to escape the Galaxy, once the Galactic rotational velocity and objects of Large Magellanic Cloud origins are considered.