Covalent RNA modifications can alter the function and metabolism of RNA transcripts. Altering the RNA substrate specificities of the enzymes that install these modifications can provide powerful tools to study and manipulate RNA. To develop new tools and probe the plasticity of the substrate specificity of one of these enzymes, we examined the engineerability of the uridine-54 tRNA methyltransferase, TrmA. Starting from a mutant that remains covalently bound to its substrate RNA (E358Q, TrmA*), we were able to use both rational design and a high-throughput sequencing assay to examine the RNA substrates of TrmA*. Although rational engineering substantially changed TrmA* specificity, the rationally designed substrate mutants we developed still retained activity with the wild-type protein. Using high-throughput substrate screening of additional TrmA* mutants, we identified a triple mutant of the substrate RNA (C56A;A58G;C60U) that is efficiently trapped by a TrmA* double mutant (E49R;R51E) but not by the wildtype TrmA*. This work establishes a foundation for using protein engineering to reconfigure substrate specificities of RNA-modifying enzymes and covalently trap RNAs with engineered proteins.