Errors arising from finite sample size and structure effects, sample displacement, background noise level, and other imperfections, often confronted in high-sensitivity magnetization measurements, are characterized. A semianalytical finite-element analysis code is developed in MATHCAD, MAPLE, and C to simulate the response of a second-order gradiometer pickup coil assembly (for example, the Quantum Design magnetic property measurement system MPMS® XL). The flux integrals are computed for given sample shape, orientation, and position, arbitrary direction of the magnetization, and magnetic moment spatial distribution, and their axial distributions are analyzed using all three standard regression procedures (geometrical average, linear regression, nonlinear least squares). Procedures are described for recovering the component of the magnetic moment orthogonal to the axis of the gradiometer, estimating the axial projection of the total dipole density, and reconstructing the on-axis magnetization profile by various types of deconvolution. The procedures are illustrated with reference to measurements of ferromagnetic thin films on diamagnetic substrates, diamagnetic wires, and discreet distributions of magnetic moments.