A small amount of oil can also act as a lubricant to help untangle knots.

Lay the necklace flat.
Apply a tiny drop of baby oil, olive oil, or even Windex (which can act as a lubricant) directly onto the knot using a cotton swab.
Let the oil penetrate for a few minutes.
Use two needles or pins, as described in Solution 1, to gently tease the lubricated knot apart.
Once untangled, clean the necklace thoroughly with a jewelry cleaner or mild soap and water appropriate for the metal to remove the oil residue.

N/A - Provides lubrication similar to powder but may require more thorough cleaning afterward.

Apply Oil and Use Pins