Rotational spectroscopy has been used. Due to the small size, rotational transitions fall in the of the visible range for the H–H pairs, whereas for ordinary molecules they would be in the GHz (microwave) range.
Otherwise, laser time-of-flight has been most often used in the "Coulomb Explosion" experiments. When laser photons remove electrons from the H–H pairs (or larger fragments) in the ultra-dense clusters, the ions will repel each other by Coulomb repulsion, and by measuring the kinetic energy of the fragments it's possible to see that the bond energy was much higher than with ordinary molecules.
A more accessible method would be observing nuclear reactions, since it is argued that they are easily possible only if the hydrogen atoms are at a very close distance with each other.
I think all of these methods are outside the scope of this thread, which was initially started because information on the catalysts used for UDH production wasn't too well known. With the recent publication of a paper dedicated on the catalysts by Holmlid et al., it has probably run its course.