Jewish Homes had a discussion of the following issue before Chanukah 5761/2000:

The wax from their candles had dripped on their silver and patina menorahs. They asked about the best way to clean those menorahs without damaging them.

Jewish Homes readers "waxed" eloquent with suggestions. This is a compendium of the reader responses on that, er, burning issue.

• Use hot soapy water and let them soak until the wax melts off - or add more hot water until it does. The hot soapy water will NOT hurt the Menorahs.
  - Submitted by Errol
• Let the candles inside the freezer before lighting. This way, they don't drop. And there is almost nothing to clean afterwards.
  - Submitted by Cristine Sauter
  
  

Either heat or cold

• Put them in the freezer for a bit, and then most of the wax chips off cleanly. Alternatively, dunk the menorah in hot water, and the wax floats to the surface. The latter method is preferred, since it doesn't take up room in the freezer.
  - Submitted by Maxine
• Use hot water. Clean it with a sponge. Be careful with the hot water.
  - Submitted by Cindy
  
• There is this stuff called Un-Do to remove candle wax. It will not damage silver or other products. You just need a little bit. It's available in craft stores
  - Submitted by Surie
• Run all of the menorot under hot (not boiling) water. Then flush the sink with grease-cutting soap and boiling water to rid the pipes of the extra wax. So far it has worked on all of my chanukiyot without hurting them.
  - Submitted by Rie Brosco
• Washing in hot water works. However, I cannot help but wonder what that wax does to my plumbing. I iron my brass and other chrome type menorahs but it should work equally well with silver. Test in an inconspicuous pot or some old flatware. Heat my iron to menorah setting - low - because wax is flammable. Iron between several layers of paper towels to absorb the melted wax. Keep using fresh paper towels. Works wonderfully.
  - Submitted by Barbara Frohlich
• On this same note - use a blow dryer to loosen the wax, and a cloth to wipe the menorah quickly. It works well.
  - Submitted by Migdalah
• Don't use hot water because it will go down the drain and you could have a serious (and expensive) problem.
  Line a cookie sheet with heavy-duty foil and place a thick layer of paper towels on top of it to absorb the melted wax. Place the menorah on top of the paper towels. Place this in a low oven (about 200F) for about half an hour. Remove it from the oven with heavy oven mitts while wiping off the last of the melted wax off.
  If you are concerned about the paper towels in the oven causing a fire, wrap the menorah in the paper towels, and then wrap that in foil.
  - Submitted by Mimi Hiller