The characteristic of being delicate; fragility(noun)
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Use "delicateness" in a sentence
"The animal body is not apart from the beauty of the human soul any more than the fragrance and delicateness of the apple blossom, and the sweetness of the ripe apple, are separable from the earth and soil and sunlight from which they are created."
"In my garden, as in my wardrobe, there are the pastel pinks that do give off a delicateness that obviously offends the author, but I frankly think of it as soothing to the eye."
"I tried, as only a young girl can, to live up to the delicateness of my name."