Special equipment: a long wooden match (not as long as a fireplace match, but longer than normal)
In a 2-cup liquid measure with a pour spout, stir together the lime juice, orange liqueur and ginger beer. Place ice in two rocks glasses; divide the mixture evenly between the glasses, leaving at least 2 inches between the top of the glass and the liquid. Float a lime wheel over the ice in each glass to act as a barrier; pour the rum over the lime wheels.
Set the glasses on a heatproof surface with nothing above; place a baking sheet nearby. Using extreme caution, light a long wooden match and carefully hold it right above one of the glasses--the flame will turn a deep blue color and the top of the cocktail will ignite. Light the second cocktail, then run the match under cold water to extinguish -- simply blowing on the match is not enough because the wood soaks up the rum. Let the cocktails burn for a few seconds, then extinguish the flames by placing the baking sheet on top of the glasses and holding it there for at least 10 seconds.
Squeeze the "roasted" lime wheels into the cocktails, stir and enjoy!