Which clauses in these sentences are restrictive?
1. the girl with the golden hair is the one we are looking for.
2. the dog that ate my homework is called henry.
3. i’m saving the muffins that have cherries for my sister.
4. the smile that she gave them was beautiful.

According to the definition of restrictive clauses, it is a clause which hides possible meaning of preceding subject by limiting it.
 And with its definition we can easily determine the needed clause in each sentence: 
1. The girl with the golden hair is the one we are looking for.
2. The dog that ate my homework is called Henry.
3. I’m saving the muffins that have cherries for my sister.
4. The smile that she gave them was beautiful.
As you can see it can pose as characteristic of a subject in some measure.
Do hope it will help you!