The SXS (Soft X-ray Spectrometer) onboard the coming Japanese X-ray satellite NeXT (New Exploration Xray Telescope) and the SXC (Spectrum-RG X-ray Calorimeter) in Spectrum-RG mission are microcalorimeter array spectrometers which will achieve high spectral resolution of ~ 6 eV in 0.3-10.0 keV energy band. These spectrometers are well-suited to address key problems in high-energy astrophysics. To achieve these high spectral sensitivities, these detectors require to be operated under 50 mK by using very efficient cooling systems including adiabatic demagnetization refrigerator (ADR). For both missions, we propose a two-stage series ADR as a cooling system below 1 K, in which two units of ADR consists of magnetic cooling material, a superconducting magnet, and a heat switch are operated step by step. Three designs of the ADR are proposed for SXS/SXC. In all three designs, ADR can attain the required hold time of 23 hours at 50 mK and cooling power of 0.4μW with a low magnetic fields (1.5/1.5 Tesla or 2.0/3.0 Tesla) in a small configuration (180 mmφ× 319 mm in length). We also fabricated a new portable refrigerator for a technology investigation of two-stage ADR. Two units of ADR have been installed at the bottom of liquid He tank. By using this dewar, important technologies such as an operation of two-stage cooling cycle, tight temperature control less than 1 μK (in rms) stability, a magnetic shielding, saltpills, and gas-gap heat switches are evaluated.