Several companies sell products to place inflatable devices inside the flue of wood-burning fireplaces or just below the damper. I tried one of these and couldn't get it to work well with the configuration of my firebox and damper.

So I went low-tech: A $3.39 red rubber playground ball. Deflated it. Stuffed it up the flue. Inflated it. Nice tight seal. I placed a marker on the log rack as a reminder to remove the ball before striking a match. Got soot on my hands, but, hey, that's what soap is for.

We bought a house previously occupied by a couple with a huge carbon footprint and are still adapting it to our more thrifty ways.  Among other things it has a "fireplace" consisting of some ceramic logs surrounded by natural gas piping in what was once an open hearth, with a large pilot light.  The damper is designed to be left partially open to vent the pilot's combustion products, which could include deadly CO, so until we re-engineer the fireplace (are looking into wood or pellet-burning inserts but Anchorage AK has lousy wood compared to Vermont where I hail from), we are using a black plastic garbage bag to reduce air leaks.  The colder it gets, the more strongly does this cheap rectangle of heavy mil plastic suction itself over the decorative glass fireplace door.

We could replace the pilot with an electronic ignition system and shut the flue completely (maybe by using a plastic ball!), but since we can't bring ourselves to enjoy watching the heat from hundreds of cubic feet of gas go straight up the chimney, this seems counterproductive.  Instead we'd like to use the fireplace for a back-up heating system so that when the power goes out for a week after our next 9.2 earthquake, we'll still be able to heat parts of the house.  Temps average below freezing from late September through late April here, i.e. over 1/2 the year, so backup power, heat and water is important!