Jamieson, Fausset and Brown on Hebrews 6:16

16. for confirmation--not to be joined, as English Version, to "an oath"; but to "an end" [Alford]. I prefer, "The oath is to them, in respect to confirmation (of one's solemn promise or covenant; as here, God's), an end of all contradiction (so the Greek is translated, He 12:3), or "gainsaying." This passage shows: (1) an oath is sanctioned even in the Christian dispensation as lawful; (2) that the limits to its use are, that it only be employed where it can put an end to contradiction in disputes, and for confirmation of a solemn promise.