A word that refers to a "half-smile"?

Solution 1:

"Smirk"? ;) It's often used in a sarcastic way, but not always.

But I guess there is no other word for "half-smile" in English. Especially when used in romantic situations, you need to use your imagination instead and use a metaphor. " :D

Solution 2:

Collins is happy with half-smile

a smile that is uncertain or short-lived

A related term is sly smile

a smile that shows you know something that other people do not: "I know why Chris didn't come home yesterday," she said with a sly smile.

More often than not, such a smile has a more knowing look to the eyes and is a bit less innocent in appearance.

Another term is wry smile

using or expressing dry, especially mocking, humor

While often subtle in appearance, such a smile is often described as slightly twisted

Solution 3:

Presumably you're looking for positive connotations, and linked to romanticism.

A timid / tender smile

A warm / sympathetic / fond smile

An amiable / engaging / thoughtful smile

A knowing / charming / suggestive smile

A quasi smile.

Solution 4:

Apologies to Leonardo, but I would suggest a Mona Lisa smile or a coy smile. Although the actor's lips are thicker, the expressions conveyed through the lips are identical.