We perform experiments on jammed suspensions of microgels with different constituent properties to determine their stress relaxation behavior on flow cessation. We observe that the stress relaxes through a two-step process: A rapid initial relaxation where internal stresses are trapped followed by a much slower decay. Trapped internal stresses are related to the solvent viscosity, particle elasticity, and volume fraction through a universal scaling. The second slower relaxation of the internal stress is characterized by a single exponential decay, which is independent of the preshear stress and relatively insensitive to the material properties of the microgel suspension. Particle-scale simulations are used to understand the microscopic mechanisms which drive the amplitude and the kinetics of the stress relaxation as well as the local particle dynamics in each regime. The rapid initial relaxation occurs through ballistic particle motion, where the number of contacts and average compression return to their static values but the asymmetry of the pair distribution function remains as a signature of the internal stress. (C) 2015 The Society of Rheology.