izvinjavati

1. (izvinjavati se) to apologize
   Stalno se izvinjava zbog kašnjenja. — He keeps apologizing for being late.
   Ne izvinjavaj se, nije tvoja krivica. — Don't apologize, it's not your fault.
2. (izvinjavam se) excuse me; I'm sorry
   Izvinjavam se, da li je ovo mesto slobodno? — Excuse me, is this seat free?
3. formal (+ acc., usually opravdavati) to excuse; to make excuses for
   Ona uvek izvinjava sina, šta god da uradi. — She always makes excuses for her son, whatever he does.

Izvinjavati se takes the dative for the person and zbog + genitive for the reason: izvinjavam se profesoru zbog kašnjenja. Transitive izvinjavati nekoga ('to excuse someone') is rare and bookish in modern Serbian; the usual verbs are opravdavati / pravdati nekoga.