I am replacing an electrical cooktop with a new one. The old cooktop was wired with white/black hot and the ground connected (no red). The new cooktop has white/black/red/ground. The feed is only a 2wire with ground (220v verified). What is recommended for connecting the new cooktop.

Your ONLY option is to run a new 120/240v circuit, such as 6/3NM cable if you need a 50A circuit.

Stan,

I believe a cooktop only needs 30 Amp and an Oven/Range combinition is 40 Amps.

Don, this greatly depends on the unit.
True, most cooktops are 30A, and most free standing ranges can use a 40A, there are many that require more, especially these days.

Okay,

Is that why although the NEC list 30 and 40 amp respectively, you are still directed to the plate on the unit?