Sari fabrics often feature a woven brocade border, which dressmakers employed to accent bodices and hems to great effect.
Certain sewing patterns suggested using saris, positioning the border decoration for a variety of effects.
Simplicity 1452, 1956 (source)
McCall's 5241, 1959 (source)
This design from Sears in 1956 was made in cotton with a metallic print to imitate the luxurious sari silks, "taking an air of elegance and splendor from its shimmering Indian-type design."
Sari styling was sometimes even interpreted quite literally, with sashes and drapery evoking the traditional garment:
If you're feeling inspired, you can pick up vintage silk saris quite cheaply on ebay. I've got two or three which I brought back from my travels in India a few years ago - now I finally have some ideas for what to do with them!