We report on the characterization of SixNy (Si-N) optical absorbers and support beams for transition-edge sensors (TESs). The absorbers and support beams measured are suitable to meet ultra-sensitive noise equivalent power (NEP<=10-19W/√Hz) and effective response time (τ) requirements (τ<=100ms) for space-borne far-infrared( IR)/submillimeter(sub-mm) spectrometers, such as the Background Limited far-Infrared/Sub-mm Spectrograph (BLISS) and the SpicA FAR-infrared Instrument (SAFARI) for the SPace Infrared telescope for Cosmology and Astrophysics (SPICA). The thermal response time (τ0) of an absorber suspended by support beams from a lowtemperature substrate depends on the heat capacity (C) of the absorber and the thermal conductance (G) of the support beams (τ0=C/G). In membrane-isolated TESs for BLISS, the effective response time τ is expected to be a factor of 20 smaller than τ0 because of voltage-biased electrothermal feedback operation and assumption of a reasonable open-loop gain, LI~20. We present design specifications for the arrays of membrane-isolated ultra-sensitive TESs for BLISS. Additionally, we measured G and τ0 for two Si-N noise thermometry device (NTD) architectures made using different fabrication processes: (1) a solid membrane Si-N absorber suspended by thin and long Si-N support beams and (2) a wire-mesh Si-N absorber suspended by long, and even thinner, Si-N support beams. The measurements of G and τ0 were designed to test suitability of the Si-N thermal performance to meet the demands of the two SPICA instruments. The solid membrane NTD architecture is similar to the TES architecture for SAFARI and the mesh membrane NTD is similar to that of BLISS TESs. We report measured values of G and C for several BLISS and SAFARI NTD devices. We observe that the heat capacity of the solid membrane devices can be reduced to the order of 1fJ/K at 65mK for devices that are wet etched by KOH. However, C for these devices is found to be on the order of 100fJ/K for a dry XeF2 process. The heat capacity is similarly large for the mesh devices produced with a dry XeF2 etch.