Although I could not see an example of it in the images I have of the Tomb of Hecatomnus at Mylasa, on other Hecatomnid monuments the women are often depicted in the orans or orant pose, at prayer. I've been trying to gather some of the later copies in an attempt to reconstruct the figures of Hecatomnid women that stood between the columns on the Mausoleum of Halicarnassus.
The most famous example is the colossal figure which stood between the columns on the Mausoleum of Halicarnassus, and which is identified as its builder Artemisia II of Caria:
The Mourning Women Sarcophagus from Sidon copied, in my opinion, the figures of women which stood between the columns on the Mausoleum. So it's not surprising that there is a figure on it which copied the Artemisia:
The type was also used for statues of Ada, as seen on this relief from Tegea which represents a statue of her:
We have a signed base from Delphi, showing that Satyros created portraits of the Hecatomnids, and the original should be assigned to him.
The term Mausoleum was used at first exclusively to describe the Heroon of Mausolus in Halicarnassus. The first time it was used in general to describe a large tomb was for the Mausoleum of Augustus in Rome. It's interesting that Augustus' wife Livia was depicted praying as the Artemisia Orans type:
The statue, now in the Vatican, was the victim of some over-enthusiastic modern restorations after its discovery in 1778-9 in the so-called Basilica di Otricoli. The head type is the same as the Fayum Livia in Copenhagen from Arsinoe, and Livia as Ceres from Lepcis Magna, and believed by scholars to be the latest official portrait type of Livia from Augustus' lifetime. The Vatican statue would thus show Livia as priestess of the deified Augustus, honouring her husband just as Artemisia honoured hers by building the Mausoleum of Halicarnassus as his tomb. Just as Artemisia served her deified husband, so did Livia, taking her as the model for portraits - for example, this portrait from a Julio-Claudian group in Parma:
A statue with the same body but a modern head of Ulpia Marciana and restored arms is now in Berlin:
A body from Cherchel is identical, showing that this became a standard type for Livia, since it was found with a togatus believe to Augustus:
The orans pose, although not in the Artemisia type, is also seen on a statue of Octavia in Naples (source):
It may have been found on this statue of a priestess from the Macellum at Pompeii, now in Naples, which again was heavily restored but imitates the Artemisia type. She is variously identified as Agrippina or Alleia Nigidia Maia, a priestess of the Imperial cult (JSTOR):
Another statue, sometimes called 'Octavia' formerly in the Lateran. The statue, now in the Gregoriano, has a head unrelated to the body, and a slightly higher girdling:
The same Artemisia Orans is the prototype for a basalt Agrippina now in the Centrale Montemartini found on the Celian in Rome, in a cache with other sculptures of members of the imperial family that had been subject to damnatio memoriae. The head, now in Copenhagen (detail), ironically was re-cut from one of Messalina, who had earlier suffered damnatio memoriae. The image is believed to date from late in Nero's reign, and depict Agrippina as a priestess of the Divus Claudius, whose temple was on the hill. The body is broken into some 41 pieces, but the large number of surviving statues of Agrippina suggests that most images of her were removed and stored hidden away rather than destroyed:
A heavily restored porphyry staute in the Louvre seems to have once been a Hadrianic or Antonine empress. She is recored in 1638 as in the Villa Borghese in Rome:
A variant on the type was used to represent Vestal Virgins,
Although the Herculaneum Women as portrait types was more popular - with hundreds of surviving copies as opposed to mere dozens for the Artemisia Orans type - there is evidence that the Orans type was used in the Hellenistic period, for example this small terracotta from Pergamon:
Much closer is a bronze empress from Sparta, who might be a Severan empress that suffered damnation memoriae:
Although there are degrees of variation in the statues that imitated the Artemisia type, several have a feature seen on the Mausoleum and in copies of the works of Mausoleum sculptors (for example the Serapis of Bryaxis): this is a fold in the drapery of the chiton below the clavicles. The variations in the Roman copies, like the variations on the Mourning Women Sarcophagus (below), perhaps indicate the variety of Hecatomnid women depicted between the columns of the Mausolem.
The Artemisia Type seems to have been used for priestesses, for example this one from the north of the temple of Apollo at Cyrene in the British Museum, formerly called Berenice II because of her corkscrew curls. The satue dates to AD 120-140 (source):
Another priestess, from Atrapaldo (Julio-Claudian after AD 20), shows how regularly the Artemisia-Livia Orans type was used for these women (source):
Yet another Agrippina was found at Olympia, which like the Atrapaldo priestess covers her left breast with her palla. The statue was found in a later wall near the Heraion, and may have come from a group in the Metroon. It was signed: "Dionysios / (son of) Apollonios / an Athenian / made (this)" (inv. 133). What makes this statue particularly interesting is that the head is closest to the archaising snail-curls and the sacchos normally seen on Hecatomnid portraits:
source) shows yet another Orante figure, with a lowered palla over the left arm ... Whilst a statue in the Jamahiriya Museum in Tripoli shows clinging drapery and the palla raised over the shoulder ... This Poppea Sabina at Olympia is another variant with the raised palla ... And this "Julia" in the Vatican ...
Although one can divide the figures into those that imitate Artemisia closely, and into Orans A and Orans B ... the bottom line is that this was a very popular statue type, used for Julio-Claudian women, for priestess (particularly of the Imperial cult), and then again for second century empresses. So academic articles that claim only a couple of dozen replicas of the type are nonsense - the type was more popular for depicitons of empresses than the Herculaeneum Women type. And I think the type originated with portraits of Hecatomnid women on the Mausoleum of Halicarnassus.