Abstnlct-We have made higb.resolution x-ray microcalorimeters ulioK 5nperconducting MoAn bUayers Ind Nb meander coils. The temperature sensor is a. Magnetic Penetration Thermometer (MPT). Operation Is similar to metallic magnetic calorimeters, but instead of the magnetic susceptibility of a paramagnetic alloy, we use the diamagnetic response of the 8uperconducting MoA. to selln temperature changes In an x-ray absorber. Flux-temperature responsivtty can be large for small sensor heat capacity, with enough dynamic range for appUcations. We find models ·of observed flux-temperature curves require several effects to explain flux penetration or expulsion in the microscopic devices. The superconductor is non~ local, with large coherence length and weak pInning of OUI. At lowest temperatures, behavior i.J dominated by Kreening currents that vary as a result of the temperature dependence of the magnetic penetration depth, modified by the effe~t of tbe nonuniformiry oftbe applied field occurring on a scale comparable to the coherence length. In the temperature regime where responslvity is greatest, spadal variations in the order parameter become important: both local variations as flux enterslIeaves the film and an intermediate state is formed, and globally as changing stability of the electrical circuit creates a Meissner transition and flux is expelled/penetrates to minimize free energy.Index Tt'nu--About four key words or phrases in aJphabetical order, separated by commas.