There are a few things to consider which may have an impact on your decision.
1. Do you have a safe place for the pieces when not being worn? And, I mean a safe place not a shoebox in the back of a closet.
2. Are you the type who has a tendency to lose or damage the piece?
3. Is the value substantial? Are your premiums well into the thousands?
4. Is your fear of theft, damage , or loss?
5. How many losses have you had within the past ten years?
Once you have thought about your answers to these questions (and you may have more questions to add) and put it on paper, think if you had insured them for the past ten years and that cost. Suppose the premiums are $ 5,000/yr, total cost of premiums for ten years=$50,000.00. Enough money to purchase a high quality safe and security system with quite a bit left over for additional watches or just put the amount of the annual premium in an account each year and become self insured. This may make more sense if you are careful with your things. Insurance costs over a period of time can add up to some serious money when you look at it on paper.
Now, there are some folks who absolutely should have insurance. You may be one of those who do, you have to make that call. Obviously, the peace of mind with insurance may be more important to some.
If you decide to insure, find out the replacement procedure by the insurance carrier in the event of a loss. They don't always rip off a check for the insured amount and many folks are surprised when an insurance company attempts to settle for an amount less than the insured value. Many firms are only required to replace with like kind and quality as described on your appraisal, so the appraisal should define the all pertinent facts to tighten the parameters of the insurance company's replacement and/or value. A lousy appraisal can cost you a great deal of money if the items are not described properly. A proper appraisal is the document which sets the parameters of replacement and should be viewed with the same importance as the item itself.
Think about it and then you'll know what is best for you.