Sealing stones are needed for pet capturing.
They have different level requirements, with the :
Level 1 Sealing Stone being able to capture pets up to level 40
Level 2 Sealing Stone able to capture pets up to level 60
'Level 3 Sealing Stones' able to capture pets up to level 80.
There are higher level sealing stones, but they are also unlocked as you rise in level, so that most of the time, we can use the level appropriate sealing stones on any pet that we may encounter.
It is to be noted that sealing stones, get progressively much much more expensive as their levels increase, with Level 2 sealing stones costing 100 coins, and Level 3 sealing stones costing a whopping 2000 coins!
The plus side at least, is that these stones dont get consumed by an unsuccessful capture.