The stories of engagement rings being appraised significantly higher than their actually cost are silly. There's not just a legion of idiotic jewelers out there selling jewels and precious metals at fractions of their cost. A pretty common scenario is a jeweler sells you a ring and includes a free appraisal. The appraised value is higher than what you just paid, so you walk out feeling all good for the bargain you just got. That appraisal isn't really what your ring is worth. Your ring is worth what someone will pay you for it, and nobody is paying you what your ring is appraised for.
The only thing a high appraisal does is make you pay higher insurance premiums than what you should be paying. If your ring is actually lost or stolen, your insurance company is most likely not cutting you a check for the appraised amount. Your insurance company gets you a replacement based on the description in your appraisal. Your insurance company will get its diamond way more cheaply than you can. Ultimately, the jeweler will pay even less for the replacement ring than you paid for your original ring.
So, you paid $5,000 for a ring, had it appraised for $7,500, paid 50% higher insurance premiums, and got a replacement that cost your insurance company $2,500.
If the high appraisal makes you feel special for having a more "valuable" ring or for having gotten a "bargain," then great. But the reality is that you actually don't want your ring appraised significantly higher than what it's really worth. And what it's really worth is probably what you paid ... or less. Save yourself the extra insurance premiums and get a legit appraisal.