Laue microdiffraction is used to determine the full elastic strain tensor of the γ and γ′ phases in grains of a nickel-based superalloy with a coarse-grained microstructure. A `rainbow' filter and an energy dispersive point detector are employed to measure the energy of Bragg reflections. For the two techniques, an uncertainty of ±2.5 × 10−3 Å is obtained for the undetermined crystal lattice parameter. Our measurements show that the filter method provides better confidence, energy resolution, accuracy and acquisition time. The sensitivity of each method with respect to the γ–γ′ lattice mismatch is demonstrated with measurements in samples with average precipitate sizes of 200 and 2000 nm. For the 200 nm precipitate size, the lattice mismatch is less than 2 × 10−3 Å and the dilatational strains are close to ±1.5 × 10−3 depending on the considered phase. For the 2000 nm precipitate size, the lattice mismatch is close to 8 × 10−3 Å and almost no elastic strain occurs in the microstructure.