Most advice columns suggest that there is no need to return your wedding/engagement ring to your former spouse. While the advice in these columns is based on etiquette rather than law, in this case the law also suggests that there is no obligation to return your ring.
A wedding ring is generally given as a gift, which means the person to whom it was given becomes its owner in law. When people separate, there is no requirement that gifts given between spouses are to be returned.
If you choose to keep your wedding ring, you should know that it may form part of your net family property, which is used to calculate the equalization payment payable by married spouses when they separate. If you're unclear on what an equalization payment is, you should review previous posts.
You should know that gifts and inheritances received from a third party during the marriage are excluded from a net family property calculation, as are certain insurance proceeds.
Gifts you receive from your spouse during the marriage can have an impact on your net family property, because by specifying "third party" the result is that gifts received between spouses will form part of the net family property. That means that if your spouse gives you a gift during marriage, it will increase your net family property, which could have an impact on the equalization payment.
Realistically, most people receive an engagement ring well before the date of the wedding. The engagement ring tends to be more valuable than the wedding band received on the date of marriage, which is often of a nominal value. Provided the value of the ring has not dramatically changed during the marriage, you will likely receive an equal deduction for ownership of the ring on the date of marriage and ownership on the date of separation.
Compared to other property you bring into the marriage it is unlikely that your wedding rings will form an important part of the equalization of net family properties, and hopefully won't be an area of contention. The cost of a fight over the ring, including the cost of an appraisal, may well be more than the actual value of the ring itself.