Beautiful, elegant sounding and Shakespearean - but I just can't get past the pig thing. Normally I'm not bothered by name meaning (I love the names Claudia and Cecilia with their horrible Latin meanings), but similar "Porcine" is a well known word in English , so I think some kids may become aware of the meaning of Portia.
You could consider similar Celia, which is also Shakespearean but has a lovely meaning -"heavenly"?