We present a scalable and modular error mitigation protocol for running $\mathsf{BQP}$ computations on a quantum computer with time-dependent noise. Utilising existing tools from quantum verification, our framework interleaves standard computation rounds alongside test rounds for error-detection and inherits a local-correctness guarantee which exponentially bounds (in the number of circuit runs) the probability that a returned classical output is correct. On top of the verification work, we introduce a post-selection technique we call basketing to address time-dependent noise behaviours and reduce overhead. The result is a first-of-its-kind error mitigation protocol which is exponentially effective and requires minimal noise assumptions, making it straightforwardly implementable on existing, NISQ devices and scalable to future, larger ones.