This can be done with or without the formal acceptance of tridanda sannyasa order. Anyone can just take the blessings of his Guru and leave home to go live “in the vana”, as Srimad-Bhagavatam says, meaning Vrindavana, as Srila Prabhupada explained.
Therefore both men and women can by de facto be renunciates. In India we see many advanced Vaisnavi wearing white and successfully living a life in perfect Krishna Consciousness.
If by sannyasa is meant saffron clothes, danda etcetera, we can’t find anywhere of formal sannyasa given to women. While we have bonafide women Gurus, it’s nowhere to be found bonafide sannyasinis.
We often find titles given to lady Vaisnavas like Swamini or Gosvamini, but these do not refer to a formal sannyasa initiation but rather to their spiritual qualifications of being able to control the senses. As Srila Rupa Gosvami says:
vaco vegam manasah krodha-vegam
A Gosvami is one who controls speech, mind, anger, tongue, belly and genitals.
If a Vaisnavi is able to do that, then she is rightly called a Gosvamini.
Our authorities are Guru, Sadhu and Sastra. Our personal opinions count as long as are backed up by bonafide authorities. I just read an article by a known devotee saying “I see no reason why women should be barred from accepting sannyasa.” I do see reasons and they are simple: no bonafide sources have authorized it.
Srila Prabhupada even says:
“A woman is not supposed to take sannyasa. So-called spiritual societies concocted in modern times give sannyasa even to women, although there is no sanction in the Vedic literature for a woman’s accepting sannyasa.”
(Srimad Bhagavatam”, Third Canto, Chapter 24 – Text 40)
– Manonatha Dasa (ACBSP)
9 Feb 2019