The ultimate source of consequence is your own conscience, though sadly some people don't have one. But some people who otherwise lack a conscience might still be fearful of God, and so that's why the Bible was seen as a great document to make people swear upon, once upon a time.
Though, while the fear of punishment might trump your inclination to do evil, it does not really make you a fundamentally better person. So, while this old ritual might soothe someone's need to feel trust in the person sworn in, it's really not such a great guarantee.
The ritual does several things:
- It's an attempt at manipulating the person being sworn in to uphold his oath, whether he's actually good or not, or whether he's planning on upholding his oaths or not
- It's a way to soothe the population's trust in the person, again a form of manipulation
- It's a way for higher officials too soothe their own trust in the person, and perhaps it thus serves as a form of self-delusion
- It's a nice ceremony to make people come together to witness some institution of power, though, and as such it is indeed a nice and good tradition, which I think is worthwhile to uphold in one way or another
While I have conflicting thoughts about how people are sworn in today, I can understand that the Bible does not hold as much power over most modern human beings as it used to, and especially those who simply aren't Christian at all. So, what should they swear upon? I, for one, would rather make it a book on moral philosophy that you can stand by, which you have read, and that you agree with.
With that said, I think if you really meditate on the moral philosophy of Jesus, then I'm sure that even if you're an atheist, you'll still come to the conclusion that it's not so bad after all. He was of course a complicated human being, but I think his fundamental ideas about The Golden Rule (i.e. that you should treat others as you would like to be treated yourself), and his ideas about how all people are created equal (see the rituals surrounding Maundy Thursday where he washed the feet of his disciples and told them that they should do the same to their underlings as a symbol for how everyone are created equal), as universally good principles that you don't strictly need to be religious to get behind.