Contextualized embeddings, which capture appropriate word meaning depending on context, have recently been proposed. We evaluate two methods for precomputing such embeddings, BERT and Flair, on four Czech text processing tasks: part-of-speech (POS) tagging, lemmatization, dependency parsing and named entity recognition (NER). The first three tasks, POS tagging, lemmatization and dependency parsing, are evaluated on two corpora: the Prague Dependency Treebank 3.5 and the Universal Dependencies 2.3. The named entity recognition (NER) is evaluated on the Czech Named Entity Corpus 1.1 and 2.0. We report state-of-the-art results for the above mentioned tasks and corpora.