The care, protection, or guardianship of someone, especially a child; the state of being under guard or protection.
From guard plus the suffix -age (Old French, from Latin -aticum). The suffix -age creates abstract nouns expressing condition or action.
Guardage is an old-fashioned legal term you'll see in Shakespeare and Victorian novels—modern English usually just says 'guardianship' or 'custody' instead!
Complete word intelligence in one call. Free tier — 50 lookups/day.