early 15c., "act of setting free from bondage," also "action of handing over to another," from Anglo-French delivrée, noun use of fem. past participle of Old French delivrer (see deliver). Sense of "childbirth, giving forth of offspring" is by 1570s; that of "manner of utterance or enunciation" is from 1660s. Of a blow, throw of a ball, etc., "act of sending or putting forth," from 1702. The hospital's childbirth delivery room is attested by 1849 (in early use often in a German context, translating Kreisszimmer).
c. 1300, deliveraunce, "action of setting free" in physical or spiritual senses, from Old French delivrance (12c., Modern French délivrance), from delivrer "to set free" (see deliver). Formerly also with senses now restricted to delivery: "childbirth; act of giving or transferring to another; utterance."
1580s, "mistake, error, a going wrong;" 1610s, "misbehavior, wrong or perverse course of conduct;" see miscarry + -age. In pathology, the meaning "untimely delivery" is from 1660s, on the notion of "fail to reach the intended result." Miscarriage of justice is from 1875, from the "going wrong" sense.