Sarma received the Sir J. C. Ghosh Medal in 1981 and the Young Scientist Medal from the Indian National Science Academy in 1983. UNESCO awarded him the Biennial Javed Hussain Prize in 1989 and a year later, in 1990, he received the medal of excellence from the Materials Research Society of India. The Government of India awarded him the Shanti Swarup Bhatnagar Prize in 1994 and he received the C. V. Raman Award in 2004. The year 2005 brought him three awards, the Hari Om Ashram Trust Award by the University Grants Commission, G. D. Birla Award and the Alumnus Award for Excellence in Research from the Indian Institute of Science. He received FICCI Award in 2006, TWAS Prize in Physics in 2007, the National Research Award in 2009 and H. K. Firodia Award in 2013. He was honored with the Knight of "The Order of the Star of Italy" in 2014, and an Honorary Doctorate from the Faculty of Science and Technology at Uppsala University in 2015.
Sarma, an elected Fellow of the Indian National Science Academy, delivered three INSA lectures in 2006, Dr. Jagdish Shankar Memorial Award Lecture, Professor R. P. Mitra Memorial Award Lecture  and A. V. Rama Rao Foundation Lecture. Two years later, he delivered the INSA Kotcherlakota Rangadhama Rao Memorial Lecture in 2008. Some of the other lectures delivered by Das Sarma are CSIR Foundation Day Lecture, Distinguished Public Lecture, 8th Atma Ram Memorial Lecture and the Joy Kissen Memorial Lecture, CNR Rao Prize Lecture.
He is an elected Fellow of the American Physical Society, The Academy of Sciences for the Developing World, the National Academy of Sciences, India, and the Indian Academy of Sciences and holds the fellowship of the Asia-Pacific Academy of Materials (APAM). He is also a J. C. Bose National Fellow and Homi Bhabha Fellow.