Location, location, location.
Just like real estate on the surface, the location of your mineral rights and the perceived value of the reservoirs below the surface will drive the purchase price. The fossil fuel industry is not going to die tomorrow or even the next day or the next year. The balancing of multiple forms of energy is going to take decades to change. Some parts of the equation will change faster than others, but dependent upon location.
As to your questions, there are reputable folks on the Directories tab that may be able to help you with appraisals. There is an American Association of appraisers. Where your minerals are located may indicate the number of appraisers in your area or those that are knowledgeable for that area. Appraisers can tell you the value of producing minerals and the value of non-producing minerals based upon a certain price deck at a certain point in time and give a projection for the future. What you might be offered is likely to be below that value since buyers fully intend to make a profit off of your minerals.
You need to talk to your accountant and attorney about WHY you might want to sell or hold or split the difference. Some folks need money quickly to pay medical bills. Some take a loan against their minerals and keep the mineral rights. Some have a larger financial plan or estate plan that they are working with. If you sell, you may have capital gains tax. Passing them onto heirs may be a better decision in some cases. You attorney or accountant can recommend buyers in your area. If it were me, I would probably not sell while there is a down market. There are lots of buyers out there right now that are buying for low prices hoping for an uptick in the next year or so.