There are six datasets in this contribution, all presented in the manuscript 'Micromagnetic Tomography for paleomagnetism and rock-magnetism'. The first dataset was measured with a Magnetic Tunneling Junction (MTJ) scanner using a synthetic sample after a pulsed magnetization of 1 Tesla was applied perpendicular to the surface of the sample (file names: mtj_synth_XXX). The second dataset was measured on a Quantum Diamond Microscope (QDM) using the same synthetic sample with a pulsed magnetization of 1 Tesla perpendicular to its surface (file names: qdm_synth_XXX). The four other datasets are regions on a volcanic sample that was not treated magnetically and measured with a QDM (file names: qdm_volc_areaY_XXX). For each of these datasets the following files are available: XXX_cuboids.txt contains a list of grains defined by groups of cuboids. xi, eta, and zeta define the midpoint of each cuboid that has sides 2a, 2b, and 2c, in the x, y, and z direction respectively, all dimensions are given in micrometers; the last column specifies the grain to which the cuboid belongs (particle index). XXX_BzUpGrid.txt contains the results of the magnetic surface scan of the sample in Tesla, with increasing x-coordinates in the horizontal direction, and increasing y coordinates in the vertical direction. The step size for the data-sets are as follows (all in micrometer and in both directions): mtj_synth 10 micrometer; qdm_synth 6.0 micrometer; qdm_volc 1.2 micrometer. XXX_magnetizations.txt contains the results of the magnetic inversions, i.e. the magnetizations per grain in A/m. The first column is the particle index, then the magnetizations in the x (mx), y (my), and z (mz) directions.