An insurance company will take your word on most things in your home. There's no need to have your double oven appraised -- you just enter the value on the insurance form and if it's destroyed in a fire, you'll have the cash to replace it.
A $70,000 Oriental rug is a completely different story. So is a million-dollar diamond necklace or a letter written by your great, great, great second cousin Abraham Lincoln.
Individual objects worth more than a certain dollar amount (which varies by policy) will have to be specifically reported to the insurance company. And you'll have to prove that value by handing in either a receipt or a professional appraisal. Since you'll rarely have a receipt for a family heirloom, you'll be heading to an appraiser.
It's important that the appraiser be certified. He or she should also have a good reputation -- insurance scams do happen -- along with sufficient experience in the particular category your heirloom falls into. Ideally, you'll take a first edition Moby Dick to a rare book appraiser, an original Picasso to an art appraiser, and a vintage emerald ring to a jewelry appraiser. A great way to find a reliable appraiser is through a dealer -- a book dealer, an art dealer, an estate-jewelry dealer. They'll have connections in the industry.
An appraisal will take into account several factors, including the condition of the item, the rarity and the demand (what it would go for at auction, typically). Any documentation you have on the heirloom, such as a certificate of authenticity, should be supplied to the appraiser.
Once you have your heirloom's professionally determined value, you can get it covered for that amount. There are a few ways to accomplish that.