The simplest of all antiatoms to fabricate is antihydrogen, composed of only a single positron and antiproton. This makes it the easiest complex system to study when it comes to symmetry between matter and antimatter. The Antiproton Decelerator at CERN is used to produce antiprotons and antiatoms. It works by firing high energy protons into a block of high density metal which then produces a range of secondary particles with high energy antiprotons among them. Strong electric fields are used to slow down these antiprotons (hence why its called a decelerator) so that they can be used in experiments. All aspects of antihydrogen are put under scrutiny such as band structure, band splitting, overall neutrality as well as the charge to mass ratio and magnetic moment of the antiproton. If even a small discrepancy could be found, despite how unlikely it seems at the moment, it would be the most revolutionary discovery in the last 50 years.
Previous experiments to accurately determine the hyperfine structure of hydrogen used a maser (microwave amplification by stimulated emission of radiation) however this can not be repeated for anitmatter. The entrapment zone for this experiment, being made of matter will annihilate any antimatter particle put inside it. Therefore the plan was to instead use a beam of antihydrogen atoms at extremely low temperatures in a set up similar to the one shown here (thank you to ResearchGate for that link) where the ultimately the measurements would be taken in an area without magnetic fields hopefully improving the accuracy of this test. So far all the data that has been gathered seems to imply the structure of the antihydrogen is, unsurprisingly, identical to within one standard deviation to that of regular hydrogen. In order to be sure of this result to a certainty of 99.99% it is estimated that about 8000 antihydrogen atoms will need to be analysed by spectroscopy. In the mean time I believe it is safe to say that, when it comes to the electron structure, there is no difference between hydrogen and antihydrogen.