Scyphate coins are sometimes described as cup-shaped or saucer-shaped, perhaps they would be better described as bowl shaped. The obverse of a scyphate coin is convex and the reverse is concave. Scyphate coins were struck in all metals and by many cultures including Celtic tribes, The Himyarites of Arabia, the Byzantine Empire and their successor medieval kingdoms. A photograph of a beautiful Byzantine gold scyphate histamenon nomisma can be seen above.
It is apparently difficult impress the the full designs on a scyphate coins in with single blow (Fig. 1 & 2). The complexity of striking scyphate coins may be one reason they were adopted. The design may have been an anti-counterfeiting measure.
Byzantine scyphate coins were struck with two successive blows to produce the full design. Each strike was made at an angle of about 45 degrees, opposite the other strike (Fig. 3).
While the two strikes at opposing angles would result in sharper more complete images, the results were often flawed in other ways. The two sides were often misaligned, part of the center was sometimes missing, and there was almost always a line where the impressions from the two strikes overlapped (Fig. 3 & 4).
Often one die only was used and was struck twice, rocked from one side to the other before the second strike. Occasionally two different dies were each struck once; in this case, it is not uncommon to find that dies bearing markedly different details were used. For example, in the striking of the silver trachy of John III Vatatzes of Nicaea (Fig. 5) the left-hand die depicts Christ's nimbus as having a single large pellet between double lines, while the right-hand die shows this nimbus as five pellets between single lines.
Sources:
Bendall, S. "Sigla on Palaeologan Hyperpyra" in Revue Numismatique 26 (1984), pp. 161 - 192. (Figures 1 - 5 are from this article). Available online