Genomic language models (gLMs) show potential for generating novel, functional DNA sequences for synthetic biology, but doing so requires them to learn not just evolutionary plausibility, but also sequence-to-function relationships. We introduce a set of prediction tasks called Nullsettes, which assesses a model’s ability to predict loss-of-function mutations created by translocating key control elements in synthetic expression cassettes. Across 12 state-of-the-art models, we find that mutation effect prediction performance strongly correlates with the predicted likelihood of the nonmutant. Furthermore, the range of likelihood values predictive of strong model performance is highly dependent on sequence length. Our work highlights the importance of considering both sequence likelihood and sequence length when using gLMs for mutation effect prediction.