One of the themes that turns up in much of Shakespeare's work is the idea of the heroine as the hero, for example, as in Much Ado About Nothing and As You Like It. Therefore, when considering the question of "essential womanliness" in context of Twelfth Night, Shakespeare's stance on what comprises womanliness needs to be considered along with social norms.
Viola demonstrates essential womanliness in accord with ideas of social norms by being loving, gentle, devoted, loyal, kind, compassionate and understanding. Whether she is Viola, the twin sister of the supposedly drowned Sebastian, or Cesario, the male page to Duke Orsino, she has these womanly qualities though as Cesario the page, they sometimes take a different manifestation. For instance, when Cesario/Viola is sent by the Duke to present his love message to Olivia in an act of devotion and loyalty Cesario/Viola stands at the door of Olivia's home and persists until he/she is granted entrance.
This behavior illustrates Shakespeare's aforementioned theme of the heroine as the hero. Cesario's/Viola's behavior shows the relationship between essential womanly loyalty and devotion and what is thought of as essential masculine persistence and determination, thus revealing them to be the same quality, thereby expanding the conception of essential womanliness and underscoring Shakespeare's oft repeated theme presenting the heroine as the hero.