Newport News is an independent city and there is no longer a Warwick County. Warwick County was one of the 8 original shires in Virginia but it consolidated in 1958 with Newport News taking the name of the city.
I checked at the library to be sure what records they have and marriages only go through 1896.
For marriage records from 1896-1912 you may contact the Newport News Health Department-Vital Records.
For marriage records after 1912, which it appears you fall within, you may contact the Virginia Depart of Health-Office of Vital Records which is in Richmond.
Remember copies of marriage records are only released to immediate family members for the first 50 years after date is recorded! You probably don't have to worry about that though.
Let me know if you can't find the address for the above.