In court, witnesses swear to tell the truth. That's interesting. Let's consider the consequences of taking this literally. Then, witnesses do not swear to tell what they believe, but to tell the truth. This means that even if they tell their honest opinion, they can be in violation of their oath, if their honest opinion is incorrect. This ups the ante. An oath to tell the truth imposes a particular responsibility on the speaker: not only to say what one thinks, but to make sure that what one thinks is true. Of course, if one has fulfilled one's epistemic responsibilities and one is still wrong, then one's violation of the oath is not culpable. But it is a violation of the oath nonetheless. So swearing to tell the truth, and not merely to be sincere, ups the ante. When we make a promise or a vow, it is not only our duty to refrain from consciously going against it, but it is our positive duty to take reasonable steps to ensure that we do not violate it. In the case of a promise to tell the truth, these steps will involve ensuring that there is a high probability of truth, and hence fulfilling one's epistemic responsibilities.
Interestingly, too, if we take the oath literally, then a person cannot be held to have violated her oath if she spoke contrary to what she believed but accidentally asserted the truth. At the same time, such speech is morally just as corrupt and deserving of punishment as when what is asserted is in fact false. If I have vowed never to eat meat, and I eat a veggie burger in the false belief that it is beef, while I have not broken my vow, my moral corruption is exactly like that of a vow-breaker (just as the moral corruption in attempted murder is the same as in successful murder, all other things being equal).
I don't know if the oath is to be taken literally in regard to the promise to tell the truth, but I like the idea that it is. This would also dovetail neatly with the idea that in ordinary assertion it is our moral duty to refrain from asserting the false (and not merely to refrain from insincerity).