In Pokémon Coloseum, like in the main series games, Pokémon have a 1/8192 chance of being Shiny. Likewise, there is a 1/8192 chance of a Shadow Pokémon being Shiny; however, when a Shiny Shadow Pokémon is captured, it is highly improbable that the Pokemon will retain Shininess. Conversely, when an ordinary Shadow Pokémon is captured, there is still the 1/8192 chance of that Pokémon becoming Shiny when it is sent to the player's party or the Pokémon storage system. Shininess is retained through purification. In Pokémon Colosseum, the color of a Shiny Pokémon can differ drastically from the handheld games.
In Pokémon XD, the game ensures that all Pokémon are not Shiny by recalculating the Pokémon personality value if it would result in a Shiny Pokémon. As in Pokémon Colosseum, the color of a Shiny Pokémon can differ drastically from the handheld games.