Isolated nonaxisymmetric rotating neutron stars producing continuous-gravitational-wave signals may undergo occasional spin-up events known as glitches. If unmodeled by a search, these glitches can result in continuous wave signals being missed or misidentified as detector artifacts. We outline a semicoherent glitch-robust search method that allows identification of continuous wave signal candidates that contain glitches and inferences about the model parameters. We demonstrate how this can be applied to the follow-up of candidates found by wide-parameter space searches. We find that a Markov chain Monte Carlo method outperforms a grid-based method in speed and accuracy. © 2018 authors. Published by the American Physical Society.