Different bootstrap methods and estimation techniques for inference for structural vector autoregressive (SVAR) models identified by generalized autoregressive conditional heteroskedasticity (GARCH) are reviewed and compared in a Monte Carlo study. The bootstrap methods considered are a wild bootstrap, a moving blocks bootstrap and a GARCH residual based bootstrap. Estimation is done by Gaussian maximum likelihood, a simplified procedure based on univariate GARCH estimations and a method that does not re-estimate the GARCH parameters in each bootstrap replication. The latter method is computationally more efficient than the other methods and it is competitive with the other methods and often leads to the smallest confidence sets without sacrificing coverage precision. An empirical model for assessing monetary policy in the U.S. is considered as an example. It is found that the different inference methods for impulse responses lead to qualitatively very similar results.