You are interested in a "laryngeal endoscopy" (informally called a "scoping" by Norwich owners) and to have the vet fill out the score sheet available on the website of the Norwich Terrier Club of America (NTCA):
look under "Norwich Health", then "Upper Airway Syndrome". Any vet with an endoscope should be able to score the upper airway of a Norwich; scoring does not require a specialist. Dr. Stanley and her co-investigators worked hard to make the scoring criteria as clear and as unambiguous as possible. There is also a "Visual Guide to the NTUAS Score" on the NTCA website to help your vet.
The score form mentions - as something nice to do, but not required - looking at the trachea and a retroflex view of the nasal cavity. However only a laryngeal endoscopy is necessary for a NTUAS score. Unless you specifically want these extra procedures, I recommend that you be clear with your vet that you only want a laryngeal endoscopy. A tracheal endoscopy and a retroflex view of the nasal cavity can double the price of a scoping, which will give you a shock when you pay the bill. (As it did to me!)
Scoping requires anesthesia. An "Anesthetic Protocol for Upper Airway Examination" is part of the web page "Visual Guide to the NTUAS Score" mentioned above. The anesthesia used is very light and any anesthesia risk is minimal - certainly less than the anesthesia risk of a dental cleaning. Doing an airway scoping at the same time as a dental cleaning is a possibility.
If you suspect that your Norwich may need airway surgery (most likely a sacculectomy - removal of fully everted saccules either with a scalpel or laser), you should schedule the scoping when a vet who is a surgical specialist (or a non-specialist with an interest in soft tissue surgery) is available. This way your Norwich will only need to have anesthesia once - not one time for the laryngeal endoscopy procedure, and later for the surgery. As with any surgical procedure, it is always good to find a vet who does a lot of the particular procedure. Remember that many dogs of the brachycephalic breeds - bulldogs, pugs, Boston terriers, etc - also require a sacculectomy - not just Norwich.
Regarding the price of a laryngeal endoscopy, the cheapest of which I am aware is approximately $500 (this includes pre-anesthesia blood work). This is approximate price charged by Dr. Stanley in Michigan, a non-specialist vet in Maryland with an interest in soft-tissue surgery (who also owns a Norwich), and also a vet in California. I am sure that as more Norwich owners and breeders have their Norwich scoped and compare prices, certain vets in each region will become the recommended vets for Norwich scoping and scoring.