Methods and apparatus (100,200) for estimating the gravity-free shape of a flexible object (140) such as a thin sheet of glass are provided. In certain embodiments, an estimate of the gravity-free shape is produced using a bed-of-nails (BON) gauge (100) and then the shape is measured at a higher spatial resolution using a second gauge (200), with the theoretical sag between the pins (110) of the BON gauge being subtracted from the shape measured by the second gauge. In other embodiments, shape measurements are performed on both sides of the object (140) and used to estimate the reliability of the gravity-free shape estimate. In further embodiments, the bed-of-nails gauge (100) uses a least squares minimization procedure in adjusting the heights of the pins (110).