Anas bin Malik narrates: "The Messenger of God (S) asked us, "What is most preferable for women?" We did not know what to reply, so Ali went to Fatima and asked her this question. Fatima (A) said, "Why did you not answer that it is most preferable for them that they do not see men and men do not see them." Ali returned and related this reply to the Prophet (S). The Prophet (S) asked, "Who has taught you this?" He said, "Fatima." The Prophet (S) stated, "She is a portion of me."
[Musnad; p 336, tradition 9, narrated by Hafiz abu Na'im in Hilyatu'l awliya']
Hakim al-Nishaburi narrates from Ibn Abbas:
When Fatima fell mortally ill she said to Asma b. al-Umais, "Do you realise what a distressing time has arrived for me? I must be hidden from the eyes of the people when I am carried before them." Asma said, "I swear by my life, I will make a bier for you in the shape that I saw used in Abyssinia." Fatima asked for more details, so Asma obtained some fresh wood and made a bier (taabut), and this was the first time such a device had been used (in Islam). Fatima (A) smiled when she saw it, and this was the first time I had seen her smile since her father had passed away. When she died, we carried her in the same bier and buried her at night.
[Musnad, p.429, trad.56, quoting from Mustadrak al-Sahihain]
It has also been narrated that: "A blind man came to Fatima (A), daughter of the Messenger of God (S), and Fatima veiled herself from him. The Prophet (S) asked why she had veiled herself from him, when he cannot see you. She replied, "O Messenger of God, he does not see me, but I can see him and (furthermore) he can smell fragrances." The Prophet (S) stated, "I bear witness that you are a portion of me."
[Musnad; p 336, tradition 10, quoting from al-Manaqib of Ibn Maghazali.]