The measurement of calorimetric spectra following atomic weak decays, beta (β) and electron capture (EC), of nuclides having a very low Q-value, can provide an impressively high sensitivity to a non-vanishing neutrino mass. The achievable sensitivity in this kind of experiments is directly connected to the performance of the used detectors. In particular an energy resolution of a few eV and a pulse formation time well below 1 μs are required. Low temperature Metallic Magnetic Calorimeters (MMCs) for soft X-rays have already shown an energy resolution of 2.0 eV FWHM and a pulse rise-time of about 90 ns for fully micro-fabricated detectors. We present the use of MMCs for high precision measurements of calorimetric spectra following the β-decay of ¹⁸⁷Re and the EC of ¹⁶³Ho. We show results obtained with detectors optimized for ¹⁸⁷Re and for ¹⁶³Ho experiments respectively. While the detectors equipped with superconducting Re absorbers have not yet reached the aimed performance, a first detector prototype with a Au absorber having implanted ¹⁶³Ho ions already shows excellent results. An energy resolution of 12 eV FWHM and a rise time of 90 ns were measured.