An antique diamond ring is subject to the same criteria as any other diamond ring or diamond in fact. That is to say, the value of the diamond would be judged on the quality and weight of the diamond and the ring would have the same value as any other ring of the same metal on an apple for apples basis.
The ring of course would more than likely be gold and that would have the usually value for a gold ring depending on the karat of the gold. Most antique rings tend to be 22 or more karats so are almost pure gold. This would be one of the important checks that would be done to establish the value of the ring.
The diamond itself should also be appraised to establish the weight and quality. This may involve removing the diamond from the ring and this should be done by a qualified jeweler or diamond dealer.
The cut, color, clarity and carat weight should be established as this is what will tell you the value of a diamond. Most antique diamonds are of good or fair quality with some being exceptional depending on when and where it was made. European antique diamond rings can be quite valuable in terms of the diamond.
An antique diamond ring may also have an antique value over and above the general value of the stone and ring, especially if it is over 100 years old (The true definition of an antique).
To find this out perhaps a visit to a professional qualified jewelery antique dealer would be helpful.
Finally, if you intend to keep an antique diamond ring which you have acquired then it is important that you DO get an appraisal for insurance purposes and also so that, if the time does come when you might want to sell it, you have some idea of its worth
