I don't see artisID anywhere in the Album or Song API. Albums have an artistName property, which can consist of zero or more artist names, concatenated. Same thing for the artistName on a Song. Physical albums might have multiple artists, with different artists for each song. Since MusicKit is an API, and not a relational database, it does not seem to expose the artist IDs, just the names. You might need to parse the artistName fields and perform searches on the names to retrieve their IDs -- admittedly not an optimal solution.