I would go higher than 18 inches. I recommend aquaria that are at least 20 inches tall for seahorses.
As you know, the height of the tank is important because seahorses need vertical swimming space to perform their complex mating ritual and successfully complete the egg transfer, which is accomplished while the pair is rising through the water column or drifting slowly downwards from the apex of their rise. If the aquarium is too shallow, eggs will be spilled during the transfer from the female to the male’s brood pouch, and mating becomes increasingly difficult or impossible below a certain minimum depth.
More importantly, a tall aquarium can also help protect the seahorses from depth-related health problems such as bloated pouch and certain forms of Gas Bubble Syndrome (GBS). This condition is caused by the formation of gas emboli within the blood and tissues of the seahorse, which sometimes happens due to gas supersaturation of the water but is more often associated with changes in the blood chemistry of the seahorse (i.e., acidosis).
The point is that the greater hydrostatic pressure at increased depth is known to protect seahorses against GBS, whereas the reduced hydrostatic pressure in shallow aquaria is known to be conducive to GBS. For this reason, it is important to select an aquarium at least 20 inches tall (the taller the better) for a seahorse setup.
Shallow tanks under 20 inches in height are associated with a higher incidence of gas bubble disease in seahorses. To cite just a couple of examples, Karen Brittain, the curator at Waikiki aquarium, reported chronic gas bubble disease problems with the Hawaiian seahorse (Hippocampus fisheri) when they were maintained in shallow aquaria. However, she found that gas bubble problems greatly decreased when the H. fisheri were transferred two taller tanks.
Likewise, Mic Payne (an aquaculturist who is raising several strains of cultured seahorses at the Seahorse Sanctuary) experienced recurring problems with GBD due to maintaining a population of Hippocampus subelongatus in shallow tanks only 16-inches (40 cm) deep:
"Seahorses maintained in this system are susceptible to gas bubble disease. Specimens with bubbles around the eyes or under the epidermis of the tail are readily treated with acetazolamide (Diamox tablets 250 mg). Mix a very small amount of crushed tablet with water and inject it into several glass shrimp that are then frozen. These are then fed to the target animal at the rate of two per day for four days. Bubbles disappear on the second day (Michael Payne, pers. com.)"
So if you have a choice, Haynes, it’s always better to go with the taller aquarium for your seahorses versus a shorter tank.
Best of luck with your new seahorse setup, Haynes!