How do doctors diagnose coarctation of the aorta?

Physical exam/scans: Coarctation, because it causes obstruction to blood flow through the aorta, will impede normal flow into the lower half of the body. Therefore, it can be detected by measuring accurate blood pressures in the legs and arms, and noting a severe drop-off in the legs. Ct or MRI scans are used to confirm the diagnosis and pinpoint the precise location of the coarctation.

By CT or MRI: Of the aorta or echocardiogram (less common).

Physical and Echo: A good physical exam with multiple blood pressure measurements can essentially diagnose it. With the advent of echo, i assume pretty much every cardiologist would officially diagnose with an echo (even in the most remote regions of the world).