simper \SIM-per, verb:

1. To smile in a silly, self-conscious way.
2. To say with a simper.

noun:
1. A silly, self-conscious smile.

It was more a simper than a smile; a pleased, self-satisfied simper.
— John L’Heureux, A Woman Run Mad

The women Sam usually dates simper and flutter and hang on his every word.
— Kristine Rolofson, Pillow Talk

Simper is derived from the Danish word sippe, which referred to a woman who sipped her drink in an affected manner.