Scaffold-based regenerative strategies that emulate physical, biochemical, and mechanical properties of the native extracellular matrix (ECM) of the region of interest can influence cell growth and function. Existing ECM-mimicking scaffolds, including nanofiber (NF) mats, sponges, hydrogels, and NF-hydrogel composites are unable to simultaneously mimic typical composition, topography, pore size, porosity, and viscoelastic properties of healthy soft-tissue ECM. In this work, we used cryoelectrospinning to fabricate 3D porous scaffolds with minimal fibrous backbone, pore size and mechanical properties similar to soft-tissue connective tissue ECM. We used salivary glands as our soft tissue model and found the decellularized adult salivary gland (DSG) matrix to have a fibrous backbone, 10–30 μm pores, 120 Pa indentation modulus, and ∼200 s relaxation half time. We used elastin and alginate as natural, compliant biomaterials and water as the solvent for cryoelectrospinning scaffolds to mimic the structure and viscoelasticity of the connective tissue ECM of the DSG. Process parameters were optimized to produce scaffolds with desirable topography and compliance similar to DSG, with a high yield of >100 scaffolds/run. Using water as solvent, rather than organic solvents, was critical to generate biocompatible scaffolds with desirable topography; further, it permitted a green chemistry fabrication process. Here, we demonstrate that cryoelectrospun scaffolds (CESs) support penetration of NIH 3T3 fibroblasts 250–450 µm into the scaffold, cell survival, and maintenance of a stromal cell phenotype. Thus, we demonstrate that elastin-alginate CESs mimic many structural and functional properties of ECM and have potential for future use in regenerative medicine applications.