Some follow-up thoughts on this question...

Hydrogen isn't very soluble in water. Oxygen is more so, but still sufficiently insoluble that most oxygen-breathing Earth creatures use special oxygen carrying proteins (most famously, haemoglobin) to move oxygen through their blood rather than just relying on its solubility in said blood. Ergo, it would seem that hydrogen-breathing animals would also be in great need of some gas-transport assistance.

As explored in that other question, ammonia is likely to also be quite common in a hydrogen-breather's environment, and can also be used as an electron donor for respiration, and doing so seems like a good strategy for aquatic organisms, which would therefore not need to care about efficient hydrogen transport; however, a land creature would be well advised to minimize its metabolic destruction of ammonia so as not to upset the pH and osmotic balance of its own bodily fluids.

So, what would make a good equivalent for the red-blood-cell mechanism that we use to transport oxygen for a hydrogen-breathing creature? Do they use a reversibly-binding metal-protein complex like us? Do they rely on dissolving hydrogen in non-polar vesicles? Or something else entirely?