Address the opposing party directly. Listen to the opposing party's views respectfully. At least pretend that you understand his or her point of view. Try to control your client's behavior and keep recriminations to a minimum. Try to figure out the other party's real concerns.
Understanding often leads to a solution.
Try to get it in writing. If you get the parties in a room and they hammer out a settlement, try to get something in writing before they leave. For example, if the meeting happens to take place while a court reporter is available, go on the record and read the terms of settlement and have parties acknowledge their agreement. If prior rounds of negotiations yielded a draft settlement document that has already been circulated, use it. Mark it up, make the changes, and have the parties sign before they leave your office.