SHAFAQNA (Shia International News Association) -- When Pharaoh learned that Asiyah, his wife, had embraced Moses' religion, he told her persistently to give up his religion and abandon his God but she never surrendered herself to Pharaoh's demand. Finally, Pharaoh ordered his men to tie her up under the scorching sun and put a heavy stone on her chest until she died there.
Asiya's grave is in Egypt.[i] As for when she died, we referred to historical sources to find the date of her demise but we found no information in this regard.
As for Maryam's death, there are different reports about the age at which she died. Contrary to what is reported in the Holy Scripture, the Islamic historical sources report that she died during the lifetime of Prophet Jesus at 51 or 63. Jesus (a) gave her ritual bathing[ii] and her grave is in Baitul Muqaddas.
[i] - Yaqut Hamvi, Shahabuddin Abu Abdullah Yaqut bin Abdullah, Mu'jam al-Buldan, vol.5, pg.142, Sadir Publications, Beirut, 2nd Publications, 1995.
[ii] - Kulayni, Kaafi, vol.1, pg. 459, Islamiyah Publications, Tehran, 2nd edition, 1983; Majlisi, Muhammad Baqir, Behar al-Anwar, vol.43, pg. 206, Al-Vafa Institute, Beirut, 1404 A.H.
Considering that the question consists of two parts, we will also give the answer in two parts:
A) Maryam (s.a)
The story of Maryam's life is not very clear; it is therefore difficult to give a precise account of the details of her life. As stated in the Holy Book, Maryam lived for many years after the death of Jesus. She witnessed the crucifixion of her son. However, the story regarding her life reported by Islamic sources is very different. Contrary to the Holy Book, the Islamic sources state that Maryam passed away during Jesus' lifetime. Jesus gave her ritual bathing (ghusl) and her tomb is in Baitul Muqaddas.
As for the date of her demise, there are varying reports. According to some reports, she died at the age 51 and according to some other reports she died at 63. As for the circumstances surrounding her death, there is no reliable or verifiable report about it.
B) Lady Asiya (s.a)
When Asiya, Pharaoh's wife, witnessed Moses' miracle in front of the sorcerers, her heart was lit with the light of Iman (belief in the One God). She started to believe in Moses. She was trying to hide her faith from Pharaoh but faith and love of God is not something to be concealed. When Pharaoh learned about her faith, he forbade her times and again from believing in Moses; he pressured on her to give up his religion and abandon his God but she never surrendered herself to Pharaoh's demand.
Finally, Pharaoh ordered his men to tie her up under the scorching sun and put a heavy stone on her chest and let her die there. When she was breathing the last moments of her life, she prayed to God as such: "O my Lord! Build for me, in nearness to Thee, a mansion in the Garden, and save me from Pharaoh and his doings, and save me from those that do wrong." God, the Exalted, accepted the prayer of this faithful, chaste and devoted woman and put her beside some of the best women of the world like Maryam.
Lady Asiya's grave is in Egypt.  As for the age at which she died, there is no precise information available. We referred to historical sources to find information in this regard but to no avail.
For further information about some aspects of the personality of Maryam and Asiyah (peace and blessing of Allah be upon them), refer to the following indexes:
1. The Chief of the Women of the World, Fatima and Maryam (s), question 13764 (site: 13472)
2. Lady Zainab (s.a) and the Best Women of the World, question 3718 (site: 4369)
3. The Position of Hazrat Maryam (s.a)", question 6591 (site: 8306).
 - Gospel, John 25:19
 - Kafi, vol.1, pg.459, hadith No.4; Behar al-Anwar, vol.43, pg. 206.
 - Ibn al-Faqih, Abu Abdullah Ahmad bin Muhammad bin Ishaq al-Buldan, researched by Al-Hadi, Yusuf, pg. 146, Beirut, Alam al-Kutub, T Al-Ula, 1416/1996.
 - Ibn Athir, Al-Kamil fit Tarikh, vol.1, pg. 307, Sadir Publications, Beirut, 1385 A.H.
 - Nasir al-Tawarikh, Jesus Volume, pg.113, cited from Porsman Software.
 - For example, it has been said that "One day, Maryam went out to the desert. When she reached a mountain, she decided to climb it. She felt tired while climbing. Then she went to sleep and died on the slope of the mountain. There and then, God sent down some Houris who bathed her and covered her with a white shroud. Jesus went to find her mother. He saw her mother laying clad in white sheet. He did not want to wake her up. He walked round her for a while. When it was time for his mother's prayer and iftar (breakfast), he called her but he did not get an answer. He went closer to her and called her louder but he still did not get an answer. Then he pulled off the sheet and noticed that his mother was dead. With weeping heart and tearful eyes, he picked up his mother's body and carried her to Baitul Muqaddas where he buried her." (Qesas al-Anbiya, or Stories of the Quran from Adam to the Last Prophet (pbuh), Hussein Emadzadeh, Nashr Islam, 2009). Obviously, part of this story is in contradiction with the hadith which says that Jesus gave his mother ritual bathing.
 - Tahrim: 11
 - Behar al-Anwar, vol.13, pg.164 and 165; Al-Kamil fi al-Tarikh, vol.1, pg. 183 – 185.
 - Yaqut Hamvi, Shahabuddin Abu Abdullah Yaqut bin Abdullah, Mu'jam al-Buldan, vol.5, pg.142,