uzdisati

1. to sigh
   Zašto stalno uzdišeš? — Why do you keep sighing?
   Uzdisala je dok je čitala pismo. — She was sighing as she read the letter.
2. (za + instr.) to pine for; to long for
   Već godinama uzdiše za komšinicom. — He's been pining for the girl next door for years.

In the sense 'to pine for' it takes za + instrumental: uzdisati za nekim.