A list of every Tsuburaya series ever! I think I found out who the woman is between Gridman Sigma and Reflex Mirrorman.http://www.scifijapan.com/articles/2014/01/30/tsuburaya-productions-official-english-title-list/
She's known as Rosetta the Masked Angel. 仮面天使ロゼッタ or Kamen Tenshi Rozetta.
But it might be one of the girls from Vanny Knights, 千年王国III銃士ヴァニーナイツ.But due to the low quality of the first photo, it's hard to tell.