In Romeo and Juliet, how does Juliet "test" Romeo's love for her?
Juliet's primary "test" of Romeo's love for her is indeed a difficult one.
Remember, everyone is masked; Juliet is intrigued by Romeo, but she does not know who he is. She asks her nurse (who functions somewhat like a nanny) to identify him.
The nurse tells her,
His name is Romeo, and a Montague,
The only son of your great enemy.
Juliet is devastated. She replies:
My only love sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me
That I must love a loathèd enemy (1.5.136-41).
The Capulets and the Montagues have a long history of animosity towards each other. Juliet and her nurse know that there is absolutely no way her father will approve of his daughter being in love with his mortal enemy. Moreover, Lord Capulet has already commanded that his daughter marry the man of his choice, Paris.
With these odds against her, Juliet knows that if she is to defy her family, she must be certain that Romeo loves her. As she contemplates her situation, alone on her balcony, and unaware that Romeo is hiding and listening, Juliet pleads:
O Romeo, Romeo, wherefore art thou Romeo?
Deny thy father and refuse thy name;
Or if thou wilt not, be but sworn my love
And I'll no longer be a Capulet.
[Aside] Shall I hear more, or shall I speak at this?
'Tis but thy name that is my enemy:
Thou art thyself, though not a Montague.
What's Montague? It is nor hand nor foot,
Nor arm nor face, nor any other part
Belonging to a man. O be some other name!
What's in a name? That which we call a rose
By any other word would smell as sweet;
So Romeo would, were he not Romeo call'd,
Retain that dear perfection which he owes
Without that title. Romeo, doff thy name,
and for thy name, which is no part of thee,
Take all myself (2.2.33-39)
As you can see, Juliet's "test" of Romeo is whether he will turn his back on his family. Like there impetuous "relationship," this test is not well-thought out. What exactly would a pair of elite teenagers do in the world? It's not like they have any particular skills. Romeo passes the test, but the end result is tragedy.