He promised with an oath - This a foolish and wicked oath.
To please a wanton girl, the monarch called the eternal God to witness his willingness to give her half his kingdom, Mark 6:23. It seems, also, that he was willing to shed the holiest blood it contained. An oath like this it was not lawful to make, and it should have been broken. See Matthew 14:9.

Whereupon he promised with an oath,.... On account of her fine dancing, and being extremely pleased with it himself; and the more, that it gave such pleasure to the whole court: he first promised her,
to give her whatsoever she would ask; and then repeating it, he confirmed it with an oath; adding, as Mark says, that he would give it her, even "to the half of his kingdom": a way of speaking used by princes, when they give full power to persons to ask what they will of them; and to express their great munificence and liberality; signifying, let it be ever so great, or cost what it will, though as much as half a kingdom comes to, it shall be granted; see Esther 5:3. A very foolish promise, and a rash oath these, which were made upon such a consideration, as only a fine dance. If she, as Theophylact observes, had asked for his head, would he have given it her? And if he swore by his head, which was a common form of swearing with the Jews (u), she very appropriately, though unjustly, as Dr. Lightfoot observes, answers to him; as you have swore by your head, give me John Baptist's head.
(u) Misn. Sanhedrim, c. 3. sect 2. T. Bab. Beracot, fol. 3. 1. Derech Eretz, c. 6. fol. 18. 2.

He promised with an oath to give her whatever she would ask. Herod confirms his promise by an oath. It was a common custom to reward a dancer or actor, on a great occasion like this, who pleased, and to ask what they wished. Herod knew that Salome danced because she had a request to make.