This work is motivated by the analysis of ecological interaction networks. Stochastic block models are widely used in this field to decipher the structure that underlies a network or that is shared by a collection of networks. Efficient algorithms based on variational approximations exist for frequentist inference and sometimes for Bayesian inference, but without statistical guaranties as for the resulting estimates. We propose to combine the variational estimation with a sequential Monte-Carlo algorithm to efficiently sample the posterior distribution and to perform model selection.