In addition to Feystones, Tempered monsters will also regularly drop Streamstones, which largely serve as materials in further upgrading high tier weapons and armor, but can also be used at the Elder Melder to reroll decorations. As far as materials go, there are five grades of Streamstone; Streamstone Shards, Streamstones, Gleaming Streamstones, Sullied Streamstones and Shining Streamstones. The latter two are better known as Warrior's Streamstones and Hero's Streamstones, respectively, which they'll be identified as when they're appraised, and are a matter for later. For now, only focus on the first three types.
Streamstone Shards, Streamstones and Gleaming Streamstones are all materials required to upgrade armor, with higher grade armor requiring higher grade Streamstones to upgrade. For example, Tier 5 - 6 for augments Streamstone Shards, Tier 7 for Streamstones and Tier 8 for Gleaming Streamstones. Streamstones Shards are almost always dropped by Threat Level One monsters, Streamstones by Threat Level Two monsters and Gleaming Streamstones by Threat Level Three monsters (Tempered Elder Dragons).
In addition, as mentioned above you can use these Streamstones as melding catalysts. Just talk to the Elder Melder and pick the option "First Wyverian Ritual", where you'll have three options - Spire Sorcery, Coral Concoction and Strange Stream. These use Streamstone Shards, Streamstones and Gleaming Streamstones, respectively, and produce variable grades of Feystones; Mysterious Feystones, Glowing Feystones and Worn Feystones, respectively. This is an assymetrical trade, however, as you'll also have to sacrifice Jewels you already possess to provide the Melding Points for the melding process. Essentially, view this as a way to clear your inventory of junk jewels and use them to roll up new, potentially better jewels. The results are random, however, just like their drop rates, so don't necessarily expect anything amazing every time you meld. You can meld three new Feystones at a time, and in terms of cost-effectiveness, you may as well horde lesser Feystones until you have enough to merge three new ones.
The ability to meld using Streamstones becomes available after the assignment Land of Convergence.