Recognize Good Judgment
When will you know that your children are mature enough to have an appreciation for your family's treasures? It's difficult to arrive at an answer because there's no predetermined age when a child can be relied on to exercise good, heirloom-responsible judgment. Some kids never seem to embrace the importance of family history, while others seem to have an innate appreciation for the intrinsic value of family lore and artifacts.
It might be tempting to give your young daughter your grandmother's doll collection, for example, but defining your hopes for these heirloom objects first is a good idea. Is this an item that will have a limited useful life, or is it something you want preserved for future generations? Handing your 10-year-old a beloved and battered old doll is one thing; turning over a museum-quality piece when you know it'll be exposed to everyday wear-and-tear is something else. No 10-year-old is going to remember, "Be very careful, it's valuable" every time she takes out a doll to play with it, and seriously, do you really want her to have to worry?