This paper presents a new approach to retrieve and further integrate tabular datasets (collections of rows and columns) using union and join operations. In this work, both processes were carried out using a similarity measure based on contextual word embeddings, which allows finding semantically similar tables and overcome the recall problem of lexical approaches based on string similarity. This work is the first attempt to use contextual word embeddings in the whole pipeline of table search and integration, including for the first time their use in the join operation. A comprehensive analysis of their performance was carried out on both retrieving and integrating tabular datasets, comparing them with context-free models. Column headings and cell values were used as contextual information and their impact on each task was evaluated. The results revealed that contextual models significantly outperform context-free models and a traditional weighting schema in ad hoc table retrieval. In the data integration task, contextual models also improved the results on union operation compared to context-free approaches.