Romeo controls a Storm Crow (non-artifact) and Juliet controls a Hover Myr (artifact).
Romeo pays 1B and evokes a Shriekmaw, saying “kill Hover Myr”. Juliet immediately calls a judge.
How is this backed up?

Back up to the point when the trigger is put on the stack. Let the player choose a target (likely only one in play) and give the GRV to Romeo.

Yup. Player have to be allowed to make strategic errors…and this sounds like one of them.
Dont be tempted to treat this like a dark banishing, even though thats probably how the player was thinking of it. Playing the Shriekmaw for its evoke cost was perfectly legal, despite being not such a good choice.