Naomi served in the Intelligence corps of the IDF – Israel Defence Army, at the branch of Ze’ev (Biber) Bar-Lavi. During her service, she was awarded her first certificate of excellence for research.
Immediately after her military service, she married Yosi (Winogradsky) Carmon. She undertook her academic studies while extending her family. At the beginning of her undergraduate studies, she gave birth to her oldest son, Ziv; during the first year of her Masters studies, her daughter Nogah was born, and in the first year of her doctoral studies, she gave birth to her youngest son Barak. Today (2016), her immediate family includes:
- Her husband: Yosi Carmon, Mechanical and Air Conditioning Engineer;
- Her children, their spouses and seven grandchildren:
Ziv Carmon, Dean of Research and Chaired Professor of Marketing at INSEAD, married to Avital Carmon, Architect and Leadership Coach, and father of Daniel and Yonatan;
Nogah Kerem, M.D., Pediatrician and Head of the Adolescents Unit in Bnai Zion Medical Center in Haifa, married to Raanan Cohen-Kerem, M.D., Otolaryngologist and Head of Children ENT (Ear Nose & Throat) Unit at Carmel Medical Center in Haifa, and mother of Nitai, Ido and Itamar;
Barak Carmon, Business Developer, Managing Director at JBCI Holdings, married to Orly Carmon, Lawyer and Life Coach, and father of Ethan and Avigail.
- Her sister: Ora Keren, wife of the late Yoram Keren, their three children, spouses and ten grandchildren.
- Her brother: Yosi Ben-Dov – C.E.O. and Principal of the Hebrew Reali School in Haifa and her sister-in-law, Nitza Ben-Dov – Professor of Hebrew and Comperative Literature at the University of Haifa, their three children, spouses and five grandchildren.