People who are wearing Neelam Stone should chant mantra dedicated to Shani Bhagavan. The simple Neelam Mantra should be chanted 108 times. Those people who are wearing it first time should also chant mantra and perform the required puja.
Kaka Dwajaya Vidhmahe
Kadga Hasthaya Dheemahi
Tanno Mandha Prachodayath
Related
Neelam Ratna Puja Procedure