Here in this lovely artwork by Philippe de Champaigne (1602-74), we see the aged Simeon joyfully singing his canticle while holding the infant Jesus. The Blessed Virgin Mary looks on from the left while Simeon takes in the moment he's been waiting so long for (God had promised Simeon he'd see the savior in his lifetime).
It was unnecessary for the Virgin Mary to go through the Hebrew purification ritual, because she was spotlessly pure. Here's why she did it.
"And he (Simeon) had received an answer from the Holy Ghost, that he should not see death, before he had seen the Christ of the Lord". -Lk 2:26
Here's another image of Simeon holding the Christ child from a painting by Blessed Fra Angelico (1400-55), who was an Italian Dominican Friar. His artwork from the early renaissance continues to grow in popularity for its beauty and simplicity.