Trying to replace a kitchen faucet
WD-40, A box wrench and a pair of pliers. Apply WD-40. Get the wrench on the nut and gently hold the bolt down as low as it can go. Turn your wrench while holding the bolt. Hold the bolt with the pliers harder until it frees up. Be careful to not marre the threads because you will have to bring the nut down through the damaged section if damage occurs.

A better way is to cut a slot in the bolt with a cut off disk on a grinder and use a slotted screw driver to hold the bolt in place. This method is potentially dangerous and not recommended if you are not comfortable and experienced with a grinder.