Organisms possessing genetic codes with unassigned codons raise the question of how cellular machinery resolves such codons and how this could impact horizontal gene transfer. Here, we use a genomically recoded Escherichia coli to examine how organisms address translation at unassigned UAG codons, which obstruct propagation of UAG-containing viruses and plasmids. Using mass spectrometry, we show that recoded organisms resolve translation at unassigned UAG codons via near-cognate suppression, dramatic frameshifting from at least -3 to +19 nucleotides, and rescue by ssrA-encoded tmRNA, ArfA, and ArfB. We then demonstrate that deleting tmRNA restores expression of UAG-ending proteins and propagation of UAG-containing viruses and plasmids in the recoded strain, indicating that tmRNA rescue and nascent peptide degradation is the cause of impaired virus and plasmid propagation. The ubiquity of tmRNA homologs suggests that genomic recoding is a promising path to impair horizontal gene transfer and confer genetic isolation in diverse organisms.