1. To try to get the approval of an important or well-known person by praising him or her or giving special attention to his or her desires: The waiters were fawning all over the celebrities at the high-class restaurant.

Lina actually enjoyed being fawned on by her fans.

2. To give a servile display of exaggerated flattery of affection, typically in order to gain favor or an advantage: Some of the employees fawn over the president of the company whenever he appears in person in their work areas.

Some politicians have been known to fawn over anyone with money who is willing to support their campaigns.