A guaranteed error estimator is developed to account for both time and space discretization errors in linear elastic and viscoelastic transient dynamics. The key innovation lies in the formulation of a dynamic constitutive relation error (CRE), which provides strict bounds on discretization errors. Using this error, strict upper and lower bounds on quantities of interest are obtained within a goal-oriented error estimation framework. To get the proposed dynamic CRE, a pair of dynamically and kinematically admissible solutions is required. A kinematically admissible solution is easily obtained by the post-processing of a conventional finite element solution, while getting a dynamically admissible solution is not straightforward. To this end, a novel equilibrium finite element for elastodynamics is proposed, utilizing the recently established dynamic complementary energy principle. Numerical examples are conducted to verify the proposed strict bounds and assess the performance and availability of the proposed EFEM.