Theophylact of Ohrid

But the reckless and lustful Herod feared to break his oath and therefore kills the righteous man, when he ought in this case to have violated the oath and not committed so terrible a crime (to keep an oath is not always good). A guardsman was the name for such a military man who was appointed by the community to execute and put to death criminals. One may also understand the passage under consideration in a figurative, spiritual sense. …

Commentary on Mark ↗

Ambrose of Milan

A Man's disposition ought to be undefiled and sound, so that he may utter words without dissimulation and possess his vessel in sanctification; that he may not delude his brother with false words nor promise aught dishonourable. If he has made such a promise it is far better for him not to fulfil it, rather than to fulfil what is shameful. Often people bind themselves by a solemn oath, and, though they come to know that they ought not to have made the promise, fulfil it in consideration of their oath. …

On the Duties of the Clergy, Book 3 ↗

Bede

It is usual with Scripture, that the historian should relate events as they were then believed by all, thus Joseph is called the father of Jesus by Mary herself. So now also Herod is said to be exceeding sorry, for so the guests thought, since the hypocrite bore sadness on his face, when he had joy in his heart; and he excuses his wickedness by his oath, that he might be impious under pretence of piety. Wherefore there follows, For his oath's sake, and for their sakes who sat with him, he would not reject her.

Catena Aurea by Aquinas ↗