When Bassanio and Portia speak to each other after he choses the right casket. Her monetary and psychological support of him after he finds out that Antonio's in trouble is also touching. Before he leaves, he promises her that he won't even sleep until he gets back, because he doesn't want any sleep to come between them. What with the drama of Shylock and the pound of flesh, the romantic aspect of the play is seriously underrated.
There's also Bassanio giving his manservant leave to marry Portia's lady-in-waiting, since now that Bassanio has found a wife, his manservant can now look for one as well.
Lorenzo's "How sweet the moonlight sleeps upon this bank" bit. Especially this:
Sit, Jessica. Look, how the floor of heaven
Is thick inlaid with patines of bright gold;
There's not the smallest orb which thou behold'st
But in his motion like an angel sings
Still quiring to the young-eyed cherubims,
Such harmony is in immortal souls;
But, whilst this muddy vesture of decay
Doth grossly close it in, we cannot hear it.
Depending on your point of view, the "Quality of Mercy" speech. Keep in mind, this is the only time anyone has tried to speak to Shylock on his terms. The speech can be read as Portia's acknowledgement that, okay, he's a Jew and they're Christians, but they share the same God and hope for the same Heaven.