It's like with any company you pay for a service: You have to check them out to ensure you're going to get good service.

There are basically three types of ways to protect your move.

1. All moving companies are required to offer by law to offer you a minimal amount of valuation coverage for your move. But it's really minimal, so if you have damages, you'll be reimbursed peanuts.

2. You can buy higher level of valuation coverage through the moving company. They either bear the valuation costs themselves, or they work with a third party to provide this coverage.  Be sure to know exactly what you are and aren't covered for.

3. You can buy third-party insurance yourself. There aren't a ton of options, and I would check their coverage levels VERY closely to see what is and isn't coverage. For example, if you pack a box yourself and stuff inside is damaged without clear damage to the box itself, the insurance coverage you bought won't protect you. All insurance companies are regulated by your state, so you can check them out that way as well.

This article goes into more detail of your moving insurance options.