Quantum error mitigation (QEM) presents a promising near-term approach to reducing errors when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using zero-noise extrapolation (ZNE). We implement ZNE through zero-temperature and zero-time extrapolations. The practical zero-time extrapolation developed exploits the Kibble-Zurek mechanism so that only problem-Hamiltonian rescaling is required. We conduct experimental investigations into the quantum critical and post-critical dynamics of a transverse-field Ising spin chain by examining statistics with weak and strong post-critical dynamics. We demonstrate successful mitigation of thermal noise and non-thermal errors through both of these extrapolation techniques.