As a proper 13th century lady, Margaret wears a veil. [As a widow she ought to be wearing a wimple, but I have heat issues.] When I wear my period (800 years ago today), I wear the long rectangular veil. When I wear Edwin's period (1225), I wear a barbette and fillet and an oval or circular veil over that. I do not wear a hairnet as they don't show up in the illuminations until much much later in the century. The few existing hairnets that we have are made of silk thread and are netted. I also do not wear one of those little white hats, as they don't appear in the English illuminations until after 1230. There is another style of headwear that you see occasionally in the manuscripts for the next couple of centuries, which is a linen cap like a snood. Sometimes it is portrayed with a couple of what look like strings wrapped around it. There is an extant cap, the Swedish cap of St. Birgitta, that fits with this depiction, but this style does not appear in the manuscripts until post-1250 as well.
The long rectangular veil:
My rectangular veil is approximately 80" x 22", with doubled hems. It has a center seam since it was made from two 40"x 22" pieces of lightweight white linen. I wear it by folding the front edge under by about four inches and then draping it over my head with the center seam at approximately my right ear. The right side then comes across the front and over the left shoulder. I have found that twisting the right half of the veil clockwise (i.e., outwards from my chin) keeps the edge from collapsing onto my face. I also have a lightweight off-white cashmere shawl which is slightly shorter that works as a veil in cooler weather. It has fringe, something I can document on this style of the veil until at least 1210.
In the earlier manuscripts (pre-1225) you frequently see women wearing what looks like a poncho with a hole cut into it. The artistic style is so lacking in detail that it's sometimes hard to tell which they're portraying--it could be an overgarment that also wraps around the head, it could be a very large veil with a hole for the face, it could be a veil and a wimple, or it could be the rectangular veil wrapped around the neck. That said, if you take that long rectangular veil and center it on the head, then wrap both ends around to the back, you get something that looks kind of like the manuscripts including where you see the chin and part of the neck directly under the chin. If the veil starts at the chin then it's probably a veil and wimple that is portrayed.
The short veil (and wimple):
There are three parts to the short veil--the barbette, the fillet, and the veil itself. The barbette and fillet are bands of undyed linen about an inch or so wide which are wrapped around the head and pinned in place. The barbette (French for "little beard) goes around vertically, under the chin and over the ears, while the fillet goes around horizontally, above the ears. I usually pin them together where they cross to prevent slippage. Over all of this goes the veil, placed so the hem in front is right above my eyes, and pinned on the sides to the bands underneath. The barbette and fillet are folded on the grain, while the circular veil seems to hang best when it is oriented so that the edge in front is a bias edge. The oval veil hangs nicely if it's cut on the grain. It is about 24" by 28", while the circular veil is about 28" in diameter. All the edges are rolled hems.
When I have occasion to wear a wimple, I take a circular veil, fold it on the bias, wrap it around my head in place of the barbette, and pin it in the back and where it crosses the fillet. Then I tuck it into the neckline of my gown. One could also use a rectangular piece of fabric for the wimple instead of a round one.
The other popular style in the 13th century is the short rectangular veil, hanging straight and puddling a bit on the shoulders. It is usually depicted worn without anything to secure it, but this is probably due to the artistic style as an unsecured veil would eventually fall off. Initial tests with an oval veil suggest that a fillet is prone to sliding backwards due to the weight of the veil, since it's not also anchored to the barbette, but a fillet under the veil would show on the forehead and the depictions of this type of veil show the edge of the veil at the top of the head rather than just above the browline. It's possible that like the 12th century examples there is something, possibly a cap, that the veil is pinned to that we cannot see.
There is an existing rectangular, almost square veil with a 13th century Italian provenance at the Abegg Foundation outside Bern in Switzerland. Legend has it that the veil "was handed to St. Francis just before he died by the Roman lady Jacoba di Settesoli". This particular veil is also embroidered. I wrote to Dr. Evelin Wetter, the curator of the 13th century collection at the Foundation, and it was her opinion (and was also that of Mechthild Flury-Lemberg, the former head of the textile department), that there is no reason to doubt the provenance of the veil. She says neither the veil itself (linen) or the embroidery (silk) has been radio-carbon dated, but that the style of the letters in the embroidery is consistent with 13th-15th century letters.
Manuscript images from the British Library:
Arundel 156, f. 103v, Germany, before 1236
Mary is wearing a long veil plus what looks like a small cap underneath.
Arundel 157, f. 5r England, before 1225
Mary and the woman in the "Massacre of the Innocents" miniature are both wearing what looks like long veils wrapped around their heads.
Arundel 439, f. 192, Italy, 13th century
This manuscript is a glossed Digestum Novum by Justinian, so I have no idea what is going on in this particular scene. There is a guy in vair lecturing, and there is a lady with a veil of the poncho-esque variety. The men in the picture have hats of the chaperon-worn-sideways style so this is most likely post-1250.
Edgerton 1066, f. 10v, England, 1270-1290
This is the Edgerton Psalter. Folio 10v is a portrayal of several saints--Catherine, Mary Magdalen, and Barbara on the top half. It's hard to see with the crowns in the way, but Mary's veil has a double line up at the top which might be the cloth folded back or it might be something hiding underneath the veil, like a cap. The edges on her shoulders look straight.
Edgerton 2432, f. 133v, Germany, post-1250
This is a partial psalter. Mary's veil looks very much like the edge is folded or rolled under, but I think the entire veil is rectangular here.
Harley 928, f. 7v, England, post-1275
The Harley Hours. Mary's veil looks very much like it is folded under across the top of her head and that it is much shorter on the sides than it is in the back. This could be a round or oval veil with a front fold, or the short side of a longer rectangular veil.
Harley 2449, f.167v, Netherlands, c.1276-1296
A book of prayers for saint's vigils. In this depiction of the three holy women at the tomb, note the woman in front who is clearly wearing a veil that goes across under her chin from left to right and then over her shoulder. A bit of her hair shows at the top and sides of her forehead.
Hirsch III.934, f. 40v, Austria or Germany, 1175-1200
Missal. In this miniature of the crucifixion, Mary's veil is also very clearly wrapped from left to right around her neck.
Royal 1 D X, f. 3, England, before 1220
Psalter. Mary, on top, has one of the short poncho-like veils. Below, the woman with the fashionable sleeves has what is clearly a long rectangular veil wrapped right to left and hanging behind her shoulder on the left side. http://www.bl.uk/catalogues/illuminatedmanuscripts/ILLUMIN.ASP?Size=mid&IllID=30150
Yates Thompson 2, f. 21v, Germany, before 1200
Collectar. Reading from left to right, the first woman has a red overgarment and a blue veil which is hanging behind her. The second woman has a blue overgarment and a red veil which is also hanging behind her. The third woman has a blue veil which looks like it is wrapped around somehow from the right and the left side is hanging behind her.