Cunnigar Hill lies behind Cunnigar Gardens in Mid Calder, overlooking the River Almond on the South bank. Cunnigar is generally not marked as a site of interest on modern maps, but the Ordnance Survey map for 1853 marks it quite clearly:

Cunnigar, OS Map for 1853
It is the location of several cist burial finds, and is also reputed to be a main local place of witch-burnings. Click here for a location map provided by StreetMap.
Cunnigar may, at first sight, seem like a Celtic placename, but is in fact probably Scots. Early spellings include Cunningry/Cunningrie (1685), and Cunningar is also know.[1]

Cunnigar, Looking West
According to John Garth Wilkinson, the name probably derives from Scots cuningar = "rabbit-warren". An alternative local name which points to the folklore surrounding the site is Witches' Knowe ("Witches' Knoll").[2]
Cunnigar is not a cairn or tumulus as such, and appears to be a natural hillock of gravely and sandy soil.

Cunnigar, Looking North-west
However, several Bronze Age cist burials were found on and near the hill in the nineteenth century. Across the hill are several indentations which may be the remnants of amateurish Victorian digs for the cist finds.

Possible C19th Excavation Site?
Equally, there are more recent attempted excavations which suggest contemporary amateur (and illegal) digs, possibly for "buried treasure", given the hill's reputation as an ancient site.

Possible Contemporary Amateur Excavation Site?
The CANMORE entry refers to a drystone wall having been built around the hillock's base, but little of this, if anything, is now visible. What can be seen are possibly two rampart-like ridges around the Eastern side of the hill, which raises questions about a possible early settlement there.

Eastern Perimeter

Eastern Perimeter
Whether or not these ridges originally extended to the Western side as well is not currently know, and in order to establish their actual significance would, no doubt, require a fuller archaeological investigation.
Local lore claims that Cunnigar, or Witches' Knowe was used as a site for witch-burning in the medieval and early modern periods, and certainly, early (albeit cursory) archaeological investigation discovered a line of charcoal and burnt shale running along the edge of the hill. More specifically, Cunnigar is said to have been to location of witch burnings during the medieval and early modern period. The so-called "trials" which preceded such a sentence were often accompanied by brutal treatment of the accused, as in the case of Margaret Thomson in 1644, who was kept awake, naked, in the Mid Calder stocks for twenty days. Fortunately for Thomson, however, she was ultimately released.
One pervasive local myth is that Cunnigar was the scene of the last witch burning in Scotland, the victim being one Lizzie Bryce (1776-1865), whose name is commemorated nearby in the main roundabout on the Southside of Livingston, as well as local pub and other names. It is said that Bryce was burned on Cunnigar, and her ashes thrown into the Almond below. However, this in not in fact the case, and although Bryce gained the reputation of being a witch, she died of natural causes in her own home - the last witch was in fact burned in 1727, forty-nine years prior to Bryce's birth!
footnotes
[1] John Garth Wilkinson, West Lothian Placenames (Harburn: Torphin House, 1992), p.18.
[2] ibid.