A traditional Bharathanatyam Dancer wears jewelry on both nostrils and the septum. Many choose to get their nostrils pierced since pierced jewelry "sits" better and is more comfortable. However, only a few get their septum pierced.
Typically, the septum is pierced on the "web" or the skin below the septum cartilage. It is usually positioned forward of the nostril holes, so that the backs of the nostril jewels do not interfere with the septum jewelry.
Septums can also be pierced "Thanjavur Style" where the nostrils and the septum pierces are on the same straight line. Women with this style piercing usually wear jewelry with a common long post and find it very comfortable since there are no backs of the jewelry inside the nostrils.