Not a lot is known about the festival, other than its clear relationship to Artemis. It is possible, like Eukleia, that it holds particular significance for young unmarried women. In other places in the ancient Greek world, festivals with similar names were celebrated with musical contests and offerings to Artemis. It is worth noting that this period in Delphi is closely associated with Artemis, with all of her documented festivals taking place within a month of each other.
The date for this festival is far from certain, but lies between the festivals of Eukleia and Laphria. As similary named festivals appear to have associations with brides in some places, it has been grouped alongside Eukleia. A ritual norm from Cyrene states that a bride must go down to the Nympheion to Artemis during the Artamisia, or else sacrifice to Artemis as a penalty$^{82}$. A similary named festival was held on the 27th of Anthesterion in Eretria$^{84}$, and perhaps on the 20th of Artamitios in Ialysos$^{83}$.
Artemis is honored with great respect through three different dedications corresponding to the feasts known as Eucleia, Artamitia, and Laphria.
Other regions also held festivals with the name Artamitia, or Artemisia. In Eretria, the Artemisia festival took place on the 27th of Anthesterion. The city's decree mandated the organization of a musical competition and provided lambs for sacrifice in preparation for the festival. The musical contest involved various categories, including rhapsodes, singers, and musicians playing the aulos and kithara. All contestants in the musical competition were also required to participate in the procession, ensuring a grand and vibrant celebration. The decree was inscribed on a stone stele and placed in the sanctuary of Artemis, ensuring the continuation of the festival for future generations$^{84}$. Similarly, in Ialysos, an Artamitia festival was held, and may have been observed on the 20th of Artamitios, and Artemis recieved honours that day$^{83}$.
§ 14: A bride must go down to the Nympheion to Artemis, whenever she wishes during the Artemisia, but better [as] quickly as possible. If she does not go down, she will sacrifice to Artemis as a penalty whatever [she wishes]. (95) She who has not gone down [during the Artemisia will purify the sanctuary of Artemis] and sacrifice in addition [as a penalty an adult animal].
– A Collection of Greek Ritual Norms (CGRN) – Dossier of purity regulations at Cyrene $^{82}$
Lines D7-8: A series of three festivals of Artemis are mentioned here: Eukleia, Artamitia and Laphria (see again Rougemont, p. 59, with refs.). For Eukleia, a common epithet for the goddess, see possibly here CGRN 107 (Kalaureia), lines 1-10. Note however that the Laphria are not necessarily tied to Artemis: Laphrios is notably found as an epithet of Apollo, e.g. Str. 10.2.21 and IG IX.1² 149 (Kalydon). Given the chronological sequence of the list in these lines, these must have fallen after 9 Bysios, either in that month, or during the following month of Theoxenios (this corresponded roughly to Athenian Anthesterion-Elaphebolion).
– A Collection of Greek Ritual Norms (CGRN) – Two excerpts from the dossier of regulations of the Labyadai at Delphi $^{5}$
Gods. Exekestos, son of Diodoros, proposed. So that we may celebrate the festival of Artemis in the finest way possible and that as many as possible may sacrifice, it was decided by the council and the people: (5) the city must organize a musical competition (with a budget) of a thousand drachmae for the Metaxu and the Phylake, and provide lambs in this way: during five days before the festival of Artemis, and of these two must be choice animals. The musical contest must begin on the 27th of the month Anthesterion. (10) They must organize the musical competition for rhapsodes, singers to the aulos, kithara-players, singers to the kithara and parody-singers. All those competing in the music contest must (also) compete in the processional ode for the sacrifice in the courtyard with the same equipment that they have in the contest.
[…]
All the contestants in the musical competition must also participate in the processsion, (40) so that the procession and the sacrifice be as beautiful as possible. The decree is to be written up on a stone stele and erected in the sanctuary of Artemis, so that the sacrifice and the music festival for Artemis will proceed in this way for all time, while the people of Eretria are free and fare well and rule themselves.
– A Collection of Greek Ritual Norms (CGRN) – Decree concerning the festival of the Artemisia at Eretria $^{84}$