The standard approach to mitigate errors made by an automatic speech recognition system is to use confidence scores associated with each predicted word. In the simplest case, these scores are word posterior probabilities whilst more complex schemes utilise bi-directional recurrent neural network (BiRNN) models. A number of upstream and downstream applications, however, rely on confidence scores assigned not only to 1-best hypotheses but to all words found in confusion networks or lattices. These include but are not limited to speaker adaptation, semi-supervised training and information retrieval. Although word posteriors could be used in those applications as confidence scores, they are known to have reliability issues. To make improved confidence scores more generally available, this paper shows how BiRNNs can be extended from 1-best sequences to confusion network and lattice structures. Experiments are conducted using one of the Cambridge University submissions to the IARPA OpenKWS 2016 competition. The results show that confusion network and lattice-based BiRNNs can provide a significant improvement in confidence estimation.