c. 1200, "protector, defender," from Old North French warant "defender; surety, pledge; justifying evidence" (Old French garant), from Frankish *warand, from Proto-Germanic *war- "to warn, guard, protect" (source also of Old High German werento "guarantor," noun use of present participle of weren "to authorize, warrant;" German gewähren "to grant"), from PIE root *wer- (4) "to cover."
Sense evolved via notion of "permission from a superior which protects one from blame or responsibility" (early 14c.) to "document conveying authority" (1510s). A warrant officer in the military is one who holds office by warrant (as from a government department), rather than by commission (from a head of state).
late 13c., "to keep safe from danger," from Old North French warantir "safeguard, protect; guarantee, pledge" (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; warrantable.