We present two novel schemes for refractometry based on a long-period fiber grating- (LPG-) based Michelson interferometer. These schemes are designed to overcome the measurement dependence of previously demonstrated LPG-based refractometry on the immersion depth. The first utilizes an unshielded LPG and the second, a shielded one. Both schemes were tested over a certain refractive-index range, and the measurement of glucose concentration in water was experimentally demonstrated. In addition, the temperature sensitivity of the two schemes is discussed.