Even in this modern age, candles are routinely used for both practical and decorative reasons. When candles break, the wick is either severed and the candle is in two pieces, or the candle is in two pieces while the wick is still intact. Either way, the candle is not necessarily rendered useless. There are a couple of ways to mend broken candles, primarily with a lighter or hot water.
If the Wick Is Severed
Fill a small pot or pan with water and set it on the stove on high heat. Water has reached a temperature of 160 to 180 degrees Fahrenheit once it begins to "dance" from the heat and this is sufficient, since the melting point of most wax candles is between 125 and 155 degrees Fahrenheit. Use a thermometer to check the water temperature if you like.
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Dip the broken ends of the candle into the pot until the wax begins to melt. For thin candles, a few seconds should be enough time; wait longer for thicker, denser candles. Be sure not to dip the candle too far into the pot, as only the outermost ends of the pieces need to be melted.
Immediately secure the two pieces together in their original form as soon as the pieces are taken out of the water. Hold together firmly for 30 seconds and set gently on a table to air dry. While 30 seconds may not be long enough for the candle to dry entirely, it will be secure enough to be set down if it is done gently. Full drying time depends on the thickness of the candle, but a few minutes should work for most candles.
If the Candle Is Broken, But the Wick Is Intact
Place some newspaper or an old cloth on a table. Place the two pieces together and stand the candle right side up on the table with one hand.
Bend the top piece back so as to fully expose the the two broken ends of the candle. With the other hand, strike a lighter and hold the flame up against the broken ends, waving the flame from side to side until the wax starts to melt, which should only take a few seconds.
Set down the lighter once the wax begins to melt and immediately bond the two pieces by holding them together with your hands for 30 seconds.