Thank you for reaching out with these questions!

I'm including some specific products as examples and to help me explain the process, not as product endorsements. Please see the important notes at the bottom of my response. 

Please be aware that beeswax is flammable and take precautions to avoid burns and fires.

Wax rendering:

Gary Reuter was the University of Minnesota Bee Lab's technician for many years, and he and his wife Ginger have a recorded presentation preparing beeswax candles: Value Added Beeswax Candle Making

Virginia Webb is well known from winning entries and judging American Beekeeping Federation's Honey Show. Here is here video on Preparing Honey Show Entries -- Beeswax Candles.

I'm pretty sure I have the most experience on our MSU team in cleaning beeswax so it can be used for candles, etc. I know some people use cheesecloth, but in my experience, it lets too much debris to pass through. The best way I've found to clean beeswax is to filter it through a felt maple syrup filter and then through a paper towel. Here is what works for me:

1. I warm beeswax that needs to be cleaned in a Presto Pot (always being very careful not to overheat it!). In a second Presto Pot with a spout (like this one: 5 Quart Beeswax Melter | Mann Lake Ltd.), I secure a maple syrup felt filter to the edges with clothespins.

2. I pour the warmed beeswax in the first Presto Pot through the maple syrup felt filter in the second presto pot. I keep this wax warm as well.

3. I secure paper towels to silicone bread molds with clothespins. I carefully pour the beeswax that was filtered through the maple syrup felt filter through the paper towel into the silicone mold. In case you're curious, I usually use paper towels that are Kirkland brand from Costco.

Liquefying honey:

I've also found that sometimes crystallized honey remains with crystals on the bottom of the container even after warming the honey. Here are some of my thoughts and tips:

I personally think it's easiest to store honey in food grade 5-gallon buckets instead of bottled in jars. Even if there are some persistent crystals in the bottom, I can avoid transferring those crystals when I transfer honey to a bottling tank. I try to wait to bottle honey until just before I plan to distribute it. 

There are lots of ways to warm honey buckets to liquefy honey. I've had the best experience using a water bath. Here is an example: Pail Warmer - 4 or 6 Pails - Maxant Industries | Beekeeping Equipment & Supplies). 

I have also heard from beekeepers who raise the temperature of the honey to about 140F for short periods. The beekeepers I've heard from who do this are larger scale beekeepers with equipment to quickly lower the honey temperature after raising it. Honey heated to 140F would stay hot for a while without a method to quickly cool it. 

Honey heated to hot temperatures may become darker in color. If heated too hot for too long, the flavor can also change and it can have burnt taste to it.

Honey heated to hot temperatures may lose some of its beneficial properties.

Important notes:

The information provided is believed to be accurate but is in no way guaranteed. The author assumes no liability in connection with any use of the products discussed and makes no warranty (expressed or implied) in that respect; nor can it be assumed that all safety measures are indicated herein or that additional measures may be required. The user, therefore, must assume full responsibility, both persons and property, for the use of these materials including any which might be covered by a patent.

This information is for educational purposes only. Reference to commercial products or trade names does not imply endorsement by MSU Extension or bias against those not mentioned.

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Please feel free to reach out with follow up questions or your own tricks and tips! Happy beekeeping!