Frankly, it's probably not necessary to have insurance on the ring. (And that's much nicer than what I first intended to write.) Insurance on items should be happening only if losing/damaging the item would be financially devastating, ie you're not in a position to replace or go without. (See: homeowner's insurance) If the ring was lost it would be possibly devastating, but mostly emotionally, and getting the same kind of ring/style as a replacement wouldn't be the same as having the old one, right? I think there are some appropriate ring-care measures to take: ie, cleaning it regularly, making sure it's properly sized and won't fall off, but beyond that it's an ornament and it's value is mostly symbolic. (Maybe I'm wrong and this ring is worth like ... 20K, in which case, eye roll.)
I'm a bit biased -- my engagement ring (which my fiance and I picked out together) was slightly under 1K, and I totally love it and it makes me happy to see it on my hand every day. BUT I think I felt like I needed a ring because after 4.5 years together, getting 'engaged' was mostly a formality, and I did worry a bit that people would think nothing had changed in our relationship without the ring. So frankly if I could go back in time I'd just get a simple small band, and wear that. But my feeling about the ring is that, while I love it, insuring it would be quite silly (unless it cost nothing additional to whatever policy I had on my home, for instance) since what I would lose if I lost it wouldn't be the cost of the ring, but rather the emotional attachment. And then life would move on, and I would just wear a simple band.