Meteorites can contain a wide range of material phases due to the extreme environments found in space and are ideal candidates to search for natural superconductivity. However, meteorites are chemically inhomogeneous, and superconducting phases in them could potentially be minute, rendering detection of these phases difficult. To alleviate this difficulty, we have studied meteorite samples with the ultrasensitive magnetic field modulated microwave spectroscopy (MFMMS) technique [J. G. Ramírez, A. C. Basaran, J. de la Venta, J. Pereiro, I. K. Schuller, Rep. Prog. Phys. 77, 093902 (2014)]. Here, we report the identification of superconducting phases in two meteorites, Mundrabilla, a group IAB iron meteorite [R. Wilson, A. Cooney, Nature 213, 274-275 (1967)] and GRA 95205, a ureilite [J. N. Grossman, Meteorit. Planet. Sci. 33, A221-A239 (1998)]. MFMMS measurements detected superconducting transitions in samples from each, above 5 K. By subdividing and remeasuring individual samples, grains containing the largest superconducting fraction were isolated. The superconducting grains were then characterized with a series of complementary techniques, including vibrating-sample magnetometry (VSM), energy-dispersive X-ray spectroscopy (EDX), and numerical methods. These measurements and analysis identified the likely phases as alloys of lead, indium, and tin.