They claim they've measured a heat excess, so I assumed some sort of calorimeter would be what they were using.

Besides, to be fair, I can think of several ways that arrangement could yield inconclusive or misleading results, both false positives and negatives.

To begin with, the fusion reaction might be real, but so inefficient (so few nuclei are involved), that not enough heat is released to be measurable at all. Chemical analysis of the residue for fusion products would be much more sensitive to micro-reactions. Also, if external energy is introduced into the system in a bound state (like the H1 trapped in the Palladium lattice I alluded to earlier) and then released by
subsequent events in the experiment, the resulting spike in heat could be mistaken for evidence of a low-yield fusion event.

Experiments of this sort were conducted in the the 30s to prove the concept of nuclear fission and calculate the energies released. There is no reason they couldn't be done today with our much-improved quantitative analysis techniques.