Dear N__:

You wrote:

>>Which sentence is correct:
>>1-The silver crown, of great sentimental value to our family, has been stolen.
>>2-The silver crown of great sentimental value to our family has been stolen.

Technically, either could be correct. A nonessential modifier is set off by commas; an essential modifier is not.

#1 means the crown has been stolen. The family has only one silver crown. The speaker also mentions in passing that the crown has sentimental value.

#2 means that a silver crown has been stolen, and that among the silver crowns that the family owns, this is the crown that is known for its sentimental value.

In everyday speech, unless you were talking about a royal family that had a collection of crowns, #1 would be the more likely scenario. How many silver crowns do most people own? 🙂

See “Commas with Nonrestrictive Modifiers” in Grammar Slammer or https://www.englishplus.com/grammar/00000081.htm for more on this.