Bower wrote (of Australian plants) [1], "There have been no systematic scientific studies of the pollination of any Calochilus species. Current knowledge is based on limited field observations
and anatomical studies. In general it is considered that most, if not all, Calochilus species are autogamous [2-5]. However, at least some species also attract scoliid wasps of the genus Campsomeris by sexual deception [3, 6, 7] allowing some outcrossing to occur. Species which attract Campsomeris wasps are therefore facultatively autogamous, self-pollination occurring if pollinia are not removed by the insect vector [3]. Calochilus species provide no nectar [3] and
have no obvious odour [3, 6].

"The column structure of Calochilus is adapted for a simple form of autogamy. In all species the anther projects forward above the stigma allowing the pollinia to fall or crumble downwards onto its upper edge. Cady [2] provided details of obligate autogamy in Calochilus campestris in populations on the south coast of New South Wales in which all ovaries developed into seed pods. After anthesis, Cady found it was impossible for an external agent to remove the pollinia. In the late bud stage the rostellum became viscid and sent out root-like growths which adhered to the apices of the pollinia. However, just prior to this the anther cells split and the pollinia began to break up, crumbling onto the upper edge of the stigmatic surface where they germinated. By anthesis the pollinia were attached firmly to both the rostellum and stigma and could not be removed.

By contrast, Fordham [6] reported that pollinia were readily removed from flowers of Calochilus campestris by the wasp Campsomeris tasmaniensis on the north coast of New South Wales.
Picked bait flowers were visited by four wasps carrying pollinaria on the front of the head, one with two sets. One was observed to both pollinate a stigma and remove the pollinarium from the same flower." ....

"The limited available observations suggest that each insect pollinated species of Calochilus attracts only sexually deceived males of a single specific Campsomeris species." In New Zealand
we don't have Campsomeris (though a similar scoliid wasp (Radumeris tasmaniensis [8]) was discovered in the Far North a few years ago).

As a consequence, all three Calochilus species found here are obliged to fall back on self pollination mechanisms. No detailed observations have been carried out on NZ Calochilus populations, but it is likely self pollination occurs as in Australia. Bruce Irwin's drawings illustrate the structures that facilitate those mechanisms.

In both Calochilus herbaceus and C. robertsonii, the anther cap is directly above the stigma, which in C. herbaceus faces downward, its upper lip curling forward under the prominent rostellum.
The mechanism described by Cady seems possible here.

In C. robertsonii, however, the stigma is saucer shaped, facing upward, so falling pollen could hardly miss it