Some monasteries found themselves needing to allow certain women into the church* for specific ceremonies. Female relatives of the founder, for example, had to be allowed to attend funerals, sometimes those of other women. The burial of nobles in monastic churches was a source of income for these communities. A few monasteries also allowed women into their churches for specific feast days, usually those associated with the Virgin Mary. Kosmosoteira was one such, and on these specific days, female relatives of monks could also meet with their kin in the courtyard under the watchful eye of the abbot.
There was also the matter of the veneration of relics, especially those known to heal. Some aristocratic women got around the problem by sending a male representative. For other women, another solution had to be found. Some monasteries kept certain relics in shrines more accessible to the public but closed off from the monastery. Others brought their relics outside on specific days so that women could reach them.
Some women entered male monasteries disguised as men. There were cases of monks sneaking prostitutes in, but there were also many instances of women disguising themselves for a more religious purpose. Some did so in order to gain access to a particular relic. A few of them had a more long-term idea in mind: becoming a monk. How many women tried or accomplished this is impossible to guess at, but it did become a popular theme in hagiography,** perhaps because it reflected the gendered tension at the heart of monastic life.
The only communities that had any success in doing that were those groups of foundations like those on Mount Athos, which barred and still bars women from setting foot on any part of the mountain. Even these, however, found themselves having to make accommodations for the female relatives of their monks by founding communities for nuns nearby.
*Either the monastic church or a secondary one at some sort of remove from the monastery proper.
**The writing of saints’ vitae or Lives.
Thomas, John and Angela Constantinides Hero, eds. Byzantine Monastic Foundation Documents: A Complete Translation of the Surviving Founders’ Typika and Testaments. Washington, DC: Dumbarton Oaks, 2000. [Text may be found here.]
Isaac Komnenos, Typikon of Kosmosoteira, 1152, translated by Nancy Patterson Sevcenko - Dumbarton Oaks
Talbot, Alice-Mary. "Women's Space in Byzantine Monasteries." Dumbarton Oaks Papers 52 (1998): 113-127.