The site of Abercorn Castle is located on the estate of Hopetoun House, just to the North-east of Abercorn itself with its ancient monastic history. Click here for a location map provided by StreetMap.
Today, all that visibly remains of Abercorn Castle in situ is a low, roughly circular mound along one of the publically-accessible pathways to the Western end of the Hopetoun House gardens:

The C18th Mound over Abercorn Castle's Ruins
Given the presence and shape of this mound, it was long thought that Abercorn Castle must have been an early motte-and-bailey structure, but under excavation by the Moray House Archaeological Society in 1963, this mound was discovered to have been an eighteenth century attempt to cover over the existence of a castle which appeared to have two main phases of construction.
Close to the castle site is an early modern wall circumnavigating this area of the Hopetoun House gardens. Given the Georgian style of the stone benches and small buildings set into it, this wall is probably of late eighteenth-century construction, but it also contains numerous large stone blocks (with a higher occurrence in the sections of wall closest to the castle site) which may or may not represent re-use of some ruined castle materials:

Garden Wall near to the Castle Site
When we visited the site, however, there was also evidence of debris from the castle being brought to the surface by rabbits burrowing beneath a large tree set on top of the eighteenth-century mound. Three small fragments were indicative, including a small piece of mortar, a periwinkle shell which had clearly been mixed in with the mortar, and a section of oyster shell. Such use of sea-shells in mortar was common practice in the medieval period, with the shells acting as a natural source of lime.
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Standard Mortar Fragment (20mm X 10mm)
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Sea-Shell Mortar Fragment (16mm X 12mm)
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(scanning resolution: 300ppi)
Evidence of such use (including whole oyster-shells) can be seen within the surviving mortar at the nearby Inchcolm Abbey, although whether our Abercorn piece represents a mortar fragment or an oyster used for food is uncertain; while the periwinkle shell was actually filled with mortar, the oyster shell below seems not to carry any mortar traces, despite being found in a small masonry assemblage which included the fragments shown above.

Oyster Shell (30mm X 34mm, Scanning Resolution: 300ppi)
The first knowledge of the castle is its ownership by William de Avenel in the twelfth century, who was presumably also the commissioner of its construction. Subsequently, it was taken over by the Graeme family, but by the fifteenth century, was in the hands of the powerful Douglases, who also owned the nearby Strathbrock Castle. During the period of Douglas ownership, the castle is thought to have undergone conversion into a manor house as was fashionable in the period. However, along with many other Douglas castles (not least Strathbrock), Abercorn fell prey to the infamous civil war between that powerful family and James II, being wrecked by the monarch on 18th April 1455 following siege.
In 1582, we find George Buchanan referring to "the half ruined castle of the Douglasses called Abercorn"[1], which would seem to indicate that James II did not completely level the castle. Certainly, Strathbrock still existed in a ruinous state as late as the nineteenth century, and so it would seem that James' reputation as a total annihilator of certain Douglas castles is unjustified.
According to The Statistical Accounts, local lore stated that the site originally dated back as far as Roman times, but the 1963 excavation yielded absolutely no Roman artefacts.
Although no major remains of the castle are to be found, two small candidates some distance from the actual site are possible remnants. Again, comparison with Strathbrock is useful. In the case of this sister castle from further South in West Lothian, again, nothing of the structure remains visibly in situ on the site itself. However, two pineapple or acorn-shaped stone gatepost caps survived to be currently displayed in the grounds of the nearby Renaissance tower house, Houstoun House. Intriguingly, two strikingly similar stones can be found being used rather less formally and more chaotically at the front and back of the same side of a gated farm wall at Parkhead, not far from the site of Abercorn Castle.

"Pineapple" or "Acorn" Gatepost Stone at Parkhead - no.1

"Pineapple" or "Acorn" Gatepost Stone at Parkhead - no.2
Given what is known about the surviving fragments of Strathbrock (click here to compare), and the fact that the latter histories of both castles are entirely coterminous (both belonging to the Douglases and both being destroyed in the same period of their civil war with James II), it is surely a rather stiking coincidence that these two sets of gatepost caps exist in these contexts. Indeed, the coincidence is so striking that chance seems unlikely. However, further research is required in order to fully authenticate the Abercorn set.
thanks to wally (livingston) for coming on the abercorn expedition with his gps technology
footnotes
[1] George Buchanan, Description of Scotland (1582), trans. Thomas Aikman, (1821), in ed. P. Hume Brown, Scotland Before 1700 from Contemporary Documents (Edinburgh: David Douglas, 1893), p.232.