We explore the effectiveness of character-level neural machine translation using Transformer architecture for various levels of language similarity and size of the training dataset on translation between Czech and Croatian, German, Hungarian, Slovak, and Spanish. We evaluate the models using automatic MT metrics and show that translation between similar languages benefits from character-level input segmentation, while for less related languages, character-level vanilla Transformer-base often lags behind subword-level segmentation. We confirm previous findings that it is possible to close the gap by finetuning the already trained subword-level models to character-level.