The curvature of a single crystal of Si with a thin epitaxial film of a SiGe alloy has been determined by measuring the spatial variation of lattice-plane orientation across the surface. The technique uses the National Institute of Standards and Technology (NIST) lattice comparator (LC) with the capability to determine the orientation of lattice planes perpendicular to a curved crystal surface with a precision of approximately 2 × 10−9 rad. The test vehicle for technique development was a NIST Standard Reference Material, SRM 2000, with a 49 nm thick film of Si–15% Ge on the surface. This alloy has a lattice parameter ≈0.6% larger than that of Si, and as the film was epitaxial with the Si substrate, the resultant stress in the Si–Ge film caused the die to be deformed into a curved shape. Measurement of the lattice-plane orientation as a function of position across the die surface allowed the die curvature to be determined, yielding a radius of curvature of 275.6 m ± 3.6 m (two standard deviations). Precise measurements were enabled in part by careful characterization of systematic variations in the LC such as the beam profile and sample-stage repeatability. From the LC plane-orientation data, the surface topography along the data line was calculated and found to be well described by a parabola, with the residual having a standard deviation less than 1 nm. More detailed examination of the LC data showed that the curvature of the die varied across the width of the die, decreasing towards the edges. Comparisons between the LC-determined topography profile and data obtained using an interferometric technique have resulted in valuable insights into issues such as establishing consistency across multiple measurement techniques, the role of within-die and within-wafer variations in curvature, and the implications of those issues for the development of standard reference materials and for the performance of devices fabricated using strain-engineering techniques.