Two-photon polymerization is a recently developed technique that is used to print millimeter-size cellular structures with micrometer resolution. The two-photon polymerization process discussed in this paper is used to build structures to stabilize direct-drive targets that are imploded at cryogenic temperatures. These targets are supported by a very thin stalk (10 to 18 µm diameter) that can be broken (or dislodged) by vibrations that occur when the target is transported or when the cryogenic shroud is removed. And any vibration at the moment of implosion affects how precisely the target is aligned to the focus of the laser beams. This study investigates the mechanical properties of different millimeter-sized cellular auxetic structures (~0.2 g/cm3) at room and cryogenic temperatures (20°C and −140°C) and how well the most promising structure dampens vibrations at room temperature.