We focus on morphological inflection in out-of-vocabulary (OOV) conditions, an under-researched subtask in which state-of-the-art systems usually are less effective. We developed three systems: a retrograde model and two sequence-to-sequence (seq2seq) models based on LSTM and Transformer. For testing in OOV conditions, we automatically extracted a large dataset of nouns in the morphologically rich Czech language, with lemma-disjoint data splits, and we further manually annotated a real-world OOV dataset of neologisms. In the standard OOV conditions, Transformer achieves the best results, with increasing performance in ensemble with LSTM, the retrograde model and SIGMORPHON baselines. On the real-world OOV dataset of neologisms, the retrograde model outperforms all neural models. Finally, our seq2seq models achieve state-of-the-art results in 9 out of 16 languages from SIGMORPHON 2022 shared task data in the OOV evaluation (feature overlap) in the large data condition. We release the Czech OOV Inflection Dataset for rigorous evaluation in OOV conditions. Further, we release the inflection system with the seq2seq models as a ready-to-use Python library.