This article explores the use of automatic sentence simplification as a preprocessing step in neural machine translation of English relative clauses into grammatically complex languages. Our experiments on English-to-Serbian and English to-German translation show that this approach can reduce technical post-editing effort (number of post-edit operations) to obtain correct translation. We find that larger improvements can be achieved for more complex target languages, as well as for MT systems with lower overall performance. The improvements mainly originate from correctly simplified sentences with relatively complex structure, while simpler structures are already translated sufficiently well using the original source sentences.