The recently developed Micromagnetic Tomography (MMT) technique combines advances in high resolution scanning magnetometry and micro X‐ray computed tomography. This allows precise recovery of magnetic moments of individual magnetic grains in a sample using a least squares inversion approach. Here we investigate five factors, which are governing the mathematical validity of MMT solutions: grain concentration, thickness of the sample, size of the sample's surface, noise level in the magnetic scan, and sampling interval of the magnetic scan. To compute the influence of these parameters, we set up series of numerical models in which we assign dipole magnetizations to randomly placed grains. Then we assess how well their magnetizations are resolved as function of these parameters. We expanded the MMT inversion to also produce the covariance and standard deviations of the solutions, and use these to define a statistical uncertainty ratio and signal strength ratio (SSR) for each solution. We show that the magnetic moments of a majority of grains under the inspected conditions are solved with very small uncertainties. However, increasing the grain density and sample thickness carry major challenges for the MMT inversions, demonstrated by uncertainties larger than 100% for some grains. Fortunately, we can use the SSR to extract grains with the most accurate solutions, even from these challenging models. Hereby we have developed a quick and objective routine to individually select the most reliable grains from MMT results. This will ultimately enable determining paleodirections and paleointensities from large subsets of grains in a sample using MMT. Plain Language Summary Iron‐bearing rocks have the ability to capture and store the direction and strength of Earth's magnetic field. This information is used to unravel the behavior of the magnetic field that protects us from harmful solar radiation. However, obtaining a reliable signal from these rocks is difficult using existing methods because many iron‐oxide grains exhibit complex magnetic behavior and obscure the magnetic information in them. To determine magnetic moments from individual grains, a new method known as Micromagnetic Tomography (MMT) has been developed. This method works similarly to imaging techniques in hospitals, but now a thin slice of rock containing magnetic grains is scanned. By using computer models we discovered that MMT is able to reliably extract magnetic signals from a majority of grains in many rock samples. Additionally, we have developed two new parameters that help us to easily select the magnetic moments of the most reliable grains in a sample. In this way, the signal of those grains can be effectively used to provide accurate information on the present and past state of Earth's magnetic field. Key Points The mathematical performance of Micromagnetic Tomography (MMT) is tested against the sample's geometry, instrumental noise and sampling interval Sample thickness and grain density are the prime factors controlling the theoretical uncertainty of magnetic moments of individual grains The mathematical accuracy of MMT results can be assessed using the signal strength ratio and uncertainty ratio