early 13c., "protector, defender," from Old North French warant (Old French garant), from Frankish *warand (cf. Old High German weren "to authorize, warrant," German gewähren "to grant"), from Proto-Germanic *war- "to warn, guard, protect," perhaps from PIE root *wer- "to cover" (cf. Latin vereri "to observe with awe, revere, respect, fear;" Greek ouros "watchman," horan "to see;" Hittite werite- "to see;" see weir).
Sense evolved via notion of "permission from a superior which protects one from blame or responsibility" (c.1300) to "document conveying authority" (1510s). A warrant officer in the military is one who holds office by warrant, rather than by commission.
late 13c., "to keep safe from danger," from Old North French warantir (Old French garantir), from warant (see warrant (n.)).
Meaning "to guarantee to be of quality" is attested from late 14c.; sense of "to guarantee as true" is recorded from c.1300. Related: Warranted; warranting.