When you combine a lower with a higher tier charm the type of lower tier charm will be upgraded to the tier of the higher tier charm. This is used to rotate your highest level charms to what you want it to be at the moment.

However just like with pulling coins there is a chance the tier of the resulting charm is actually higher than what you put in. I was trying to figure out what the limits of this are since I couldn't find any solid information.

So what I could do was.
Combining bronze with plastic until I got silver ~10 attempts
Combining silver with plastic until I got gold ~5 attempts
Combining gold with plastic until I got flawed crystal ~1 attempts

Now I know this might look insane but it was pure luck. From testing so far the closer the charms are in Tier the higher the chance for an upgrade.
I have not managed to upgrade the flawed crystal to crystal with a plastic charm yet.
This could either mean that the cap is around 5 tiers or the chance is so small it might aswell be capped.

Another test I made at higher tier levels
Combining Sapphire with emerald until I got vivid sapphire ~27 attempts
combining vivid sapphire with emerald until I got rough alexandrite ~6 attempts

(Again just my luck being stupid)
I have so far not managed to upgrade a rough alexandrite with just emerald tier either
reinforcing my believe of the cap hard or soft being at around 5 tiers

I am still testing whether current necklace level affects the chance.
Either way, if you trust your luck or are a gambling man, you might save some gold or you might lose it all.

Edit: Round 2

No Charms equipped
Painted + Plastic = Bronze ~4 attempts
Bronze + Plastic = Silver ~2 attempts
Silver + Plastic = Gold ~4 attempts
Gold + Plastic = flawed crystal ~14 attempts
flawed crystal + Plastic = crystal ~30 attempts

For the next attempts I will upgrade my necklace to vivid alexandrite level,
in hopes that it does increase the chance

crystal + Plastic = rough emerald ~28

now this ones surprising,
I dont think the higher level necklace actually helped but I will start a new round with it

Painted + Plastic = Bronze ~1 attempt
Bronze + Plastic = Silver ~1 attempt
Silver + Plastic = Gold ~12 attempts
Gold + Plastic = flawed crystal ~2 attempts
flawed crystal + Plastic = crystal ~still failed after 25 attempts

Ill use painted now since at this point I have a lot leftover

flawed crystal + painted = crystal ~another 10 attempts
crystal + plastic/painted = rough emerald ~16 painted, 15 plastic

It seems necklace level has no influence on the charm upgrades
Side note: Ive had multiple plastic coins upgrade all the way to gold at this point

Ill now attempt to upgrade a vivid alexandrite with whatever I have left laying around
~17 plastic, 3 painted, 3 bronze, 2 silver, 15 gold, 3 flawed crystal, 1 crystal , 3 rough emerald, 12 rough sapphire, 1 flawed sapphire
and that was everything I had lying around and upgrade failed