To get that last bit of tomato sauce or any other liquid out of a bottle quickly, try swinging it in a windmill motion with your hand, says YouTube user MaxMan. It causes the sauce to come towards the mouth of the bottle.
Use your shoulder as the central axis and hold the bottle with the end facing outwards. Then swing your arm in a full arc, like you're Pete Townshend. There is some debate on whether this is technically centrifugal force or centripetal force.
One full swing might not be enough — it wasn't for me — but a few swings did the trick. Alternatively, you could just put a drinking straw in the bottle to speed up the flow of ketcup.