St. Emilia is the mother of four Saints: Sts. Basil the Great, Gregory or Nyssa, Peter of Sebaste, and Macrina the Younger (the Teacher). She was also the wife of a St. Basil the Elder and daughter-in-law of a St. Macrina the Elder.
She has four Feastdays that I know of: May 8th (her repose), May 30th (with her husband), January 1st (with her son, St. Basil), and the Sunday after the Presentation of the Lord into the Temple (with the Three Holy Mothers of the Three Holy Hierarchs).
Life of St. Emilia
St. Emilia and her daughter, St. Macrina the Younger
Feastday of the Three Holy Mothers of the Three Holy Hierarchs (includes some information about St. Emilia):
Account 1
Account 2
Further details about St. Emilia may be gleaned from the life of St. Macrina (her daughter)