Either there is conflicting information or a lack of when it comes to this question. Is it allowed in NEC code to permit an over-the-range microwave to run off of one of the small-appliance branch circuits?
Folks may be too wrapped up in the kitchen rules and forgetting the everywhere rule.
No receptacles if fixed loads are >50%
Add up the rated amperage (or VA/120 or watts/120) of each and every load that is either hardwired or permanently installed like the microwave, garbage disposal, fan, lights, yadayada. Got the total?
Now look at the circuit breaker, it'll be 15 or 20 amps.
If the total of all the fixed, installed loads is more than half the circuit breaker rating, that circuit cannot power receptacles (other than the receptacles for the installed loads.)
210.52 (B)(1) says that the 20A circuits shal serve all wall and floor receptacle outlets covered by 210.52(A), all countertop outlets covered by 210.52(C), and receptacle outlets for refrigeration equipment.
210.52(B)(2) Says that the two or more small-appliance branch circuits specified in 210.52(B)(1) shall have no other outlets.
210.52(A) - General wall outlets 12' O.C.
210.52(C)(5) says that outlets not readily accessible by appliances fastened in place shall not be considered as required outlets.
Given this i take it as an above range microwave is a fastened in place appliance, therefore that receptacle is not covered by 210.52(C).
And since 210.52(B)(1) says that the 2 small appliance circuits shall only cover 210.52(A) and 210.52(C), thus a separate circuit is needed.
My answer would be that an additional circuit is required. I think if you read a bit further exception # 2 specific appliances shall be permitted to be supplied from a 15 a individual branch circuit. The built in appliances require a separate circuit in my state but if sitting on the counter the can be powered from one of the 2 small appliance circuits.
The commentary in the hand book for 210.52.B.1 states outlets in cabinets are not allowed only portable appliances used at a kitchen counter. I believe my state code follows this in requiring fixed in place appliances like microwaves, and dishwashers to be on a separate circuit from the small equipment branch circuits required.
I can only access the 2017 NEC, but I don't know of anywhere that has adopted it yet. It's likely, however, to be stricter than whichever year of the NEC is legal in your area. In the NEC 2017, it says
210.52(B)(1) Receptacle Outlets Served.
In the kitchen, pantry, breakfast room, dining room, or similar area of a dwelling unit, the two or more 20-ampere small-appliance branch circuits required by 210.11(C)(1) shall serve all wall and floor receptacle outlets covered by 210.52(A), all countertop outlets covered by 210.52(C), and receptacle outlets for refrigeration equipment.
This would appear to indicate that a separate circuit, exclusively for the microwave, is not required.