Additive manufacturing (AM) enables production of geometrically-complex elastomeric structures. The elastic recovery and strain-rate dependence of these materials means they are ideal for use in dynamic, repetitive mechanical loading. Their process-dependence, and the frequent emergence of new AM elastomers, commonly necessitates full material characterisation; however, accessing specialised equipment means this is often a time-consuming and expensive process. This work presents an innovative equi-biaxial rig that enables full characterisation via just a conventional material testing machine (supplementing uni-axial tension and planar tension tests). Combined with stress relaxation data, this provides a novel route for hyperelastic material modelling with viscoelastic components. This approach was validated by recording the force-displacement and deformation histories from finite element modelling a honeycomb structure. These data compared favourably to experimental quasistatic and dynamic compression testing, validating this novel and convenient route for characterising complex elastomeric materials. Supported by data describing the potential for high build-quality production using an AM process with low barriers to entry, this study should serve to encourage greater exploitation of this emerging manufacturing process for fabricating elastomeric structures within industrial communities.