The Cherish Ball cannot be obtained, so cannot normally be used. If it were to be obtained, when used from the Bag in a wild encounter, it would attempt to catch the wild Pokémon with a catch rate modifier of 1×.
As a Pokémon's Poké Ball
From Generation VI onward, bred Pokémon inherit their Poké Ball from their parents. However, the Cherish Ball and Master Ball cannot be passed down via breeding; instead, they act as a regular Poké Ball for inheritance purposes.