In the last several years, the need for an alternative to chemical propulsive systems for low-orbit satellite deorbiting has become increasingly evident; a Tethered System can provide adequate thrust or drag without the complications of combustions and with a minimal impact on the environment. In this context, the authors are part of a team that is studying various tether applications and building a prototype of an electrodynamic tether system. The goal of this paper is to characterize tether materials in order to find valid solutions for future space tether missions. Mission requirements (e.g., the survivability to hypervelocity impacts and the capability to damp oscillations in electrodynamic tethers) influence the choice of tether parameters such as cross section geometry (round wires or tapes), materials, length, and cross section sizes. The determination of the elastic characteristics and damping coefficients is carried out through a campaign of experiments conducted with both direct stress/strain measurements and the laboratory facility SPAcecRraft Testbed for Autonomous proximity operatioNs experimentS (SPARTANS) on a low friction table at the University of Padova. In the latter case, the stiffness and damping of a flexible line were verified by applying different tensile load profiles and then measuring the tether-line dynamic response in terms of tension spike amplitude, oscillation decay, and estimation of the damping coefficient.