Born in New York City, Sharmat attended Syracuse University as a music major. He transferred to The University of Arizona, finishing his studies at G.I.T. (now called Musicians Institute). Sharmat's early professional years were filled playing gigs and occasional sessions, moving to Las Vegas to play showroom gigs by 1983. Craig returned to Los Angeles in 1985, where he quickly landed the role of guitarist for saxman Ronnie Laws. A tour with singer Randy Crawford soon followed, though Sharmat later moved away from touring to score his first TV series, Disney's Kids Incorporated, arranging and composing the final 3 years of the series. During the same time frame, Sharmat scored the background music to the American TV series Xuxa. Since 1995, Sharmat has written music for America's Most Wanted. This show led to his finding work with Sirens Media, for which he has written the main titles and background music for The Real Housewives of New Jersey among many other shows. He also wrote the opening for the 2007 MTV Movie Awards featuring Sarah Silverman. In 2008, Sharmat scored the movie Gotta Dance, produced and directed by Academy Award nominee Dori Berinstein. Sharmat is a graduate of Spud Murphy's Equal Interval System system.

Craig has written a significant amount of music for 615 Music, a major music library based in Nashville, Tennessee.

In other activity, Sharmat also has co-written three Nate the Great children's books.