Shleigh02:We currently do not have renter's insurance, but I could consider bying some and adding the rings on as a rider.
BUY RENTER'S INSURANCE TODAY. My husband's apartment burned down a few years ago, and if he hadn't had renter's insurance, he wouldn't have been able to replace things like his couch and computer. Renter's insurance is SO cheap; there is no reason not to have it.
If your ring is not that expensive, you may be able to add a rider for next to nothing with no appraisal. Mine paid 100% to have a side stone replaced after it fell out. If any single piece of valuable property is over a threshhold amount (edit: for my policy, it's $2500), then you may have to get it appraised and buy separate coverage). I have a total of $5000 of valuable property coverage for $3/month.