As someone who has actually touched special weapons as a nuclear materials courier for NNSA/OST there have been LOTS of exploded nukes at high altitude.
Research Operations Hardtack, Argus, and Dominic(sp), and all the Soviet tests at Kapustin Yar or Novaya Zemlya (sp).
Hardtack I&II, Argus, and most of Dominic I&II were conducted far out to sea, and EMP wasn’t the focus of the test. The landbound tests in Nevada were small.
(H)EMP will be a much bigger problem than most people want to admit, if someone decides to hit us. The actual damage done will be very hard to fix in a timely manner. Taking out the power grid of much or all of the US would pretty much slide us into 2nd or 3rd world status in a very short amount of time.