pomilovati

1. to caress; to stroke
   Pomilovala je dete po kosi. — She stroked the child's hair.
   Pomilovao sam mačku i ona je zapredla. — I stroked the cat and it started purring.
2. (of a convict) to pardon
   Predsednik je pomilovao dvojicu zatvorenika. — The president pardoned two prisoners.

The imperfective for "to caress" is milovati.