While Portia's situation is different from Antonio's in that she had no say in her father's devising the casket riddles/test for her future mate, both she and Antonio are bound to someone else because of their "bonds" or "contracts." If Portia does not abide by her father's wishes, she loses everything; so she is bound to her deceased father in that way. Similarly, if she does subject herself to her father's requirements for her mate, then she is bound to her future husband to whom Belmont will be entrusted. Antonio is also under another person's control because of his contract with Shylock. If he does not fulfill his part of the contract, his life is in Shylock's hands.
Additionally, one person stands to benefit from both Portia's and Antonio's bonds--Bassanio. If Portia follows her father's will and Bassanio chooses correctly, then he will inherit all of Portia's wealth and power. By Antonio entering into the bond with Shylock, Bassanio gains access to the funds that he needs to impress Portia and win her over.