"she seemed to deserve the name of saint equally with her namesake, or with any other female in the Roman calendar "

The General Roman Calendar dedicates particular days of the year to liturgical celebrations of specific saints.  Only a relatively small proportion of saints are honoured in this way by the Roman Catholic Church, covering approximately half the year. 

The quote refers to St Bridget, or St Birgitta, celebrated on 23 July. 

Other female saints celebrated in the calendar include Agnes, Angela, Agatha, Catherine, Cecelia, Clare, Elizabeth, Felicity, Jane, Maria, Mary Magdalene, Martha, Monica, Perpetua, Rose, Scholastica, and Teresa.