In much the way that the appearance of Calpurnia humanises the character of Caesar, one of the key roles of Portia is to humanises Brutus and locate him in the home as a husband, as well as in the forum as a politician.
Portia is extremely articulate, forthright, and bold: her long, carefully poised speech to Brutus in the garden arguing (not that she should have equal rights within her marriage, but that she should know Brutus' secrets and advise him) does indeed lead to him telling her about the conspiracy.
She seems maddened - hearing noises blown by the wind, and raving on the streets - in the next (and final) scene she appears in, knowing that her husband is in danger, but unable to do anything about it. Brutus hears much later in the play (in the Act IV tent scene) that she has committed suicide by swallowing coals.
One key thing you might want to think about is a single line Brutus speaks when trying to persuade her back inside in her first scene, telling her that her "condition" should be exposed to the cold night air. What is this "condition"? Is she ill? Fiona Shaw played her on a stick as an extremely ill woman in Deborah Warner's production. Or - and this interpretation makes her suicide all the more harrowing - might she be pregnant?
As the daughter of Cato, a noble-born, Portia is an intelligent woman who demands to be an equal partner with her husband Brutus. Her argument, that she is not an ordinary woman, since Brutus chose her, in conjunction with who are family is, gives her the right to know what is going on in Brutus's life outside the home. She wants to share his life completely, as a wife. She sets out to prove to Brutus that she can handle the burden of knowing all of his secrets.
She makes it clear to her husband, that she is physically strong, to express this concept, she stabs herself in the thigh, to prove to Brutus that she is capable of bearing pain.
"Her anxiety over Brutus's mission, she also considers a weakness, as though love were a weakness."
"Her final proof of strength comes when she horribly kills herself because of Anthony's growing power which is a threat to her husband."
But once Brutus unburdens himself and tells her about the secret plan to overthrow Caesar, she cannot talk to anyone about it because she is a woman. She must keep silent. Once Brutus leaves, she is frustrated by the need to keep silent. Her horrible death, swallowing burning coals until she suffocated, is both symbolic and courageous.
Symbolically, she silences herself for good, with a method of death that obviously was excruciatingly painful.