Aminoglycoside antibiotics, which are able to selectively bind to RNA, are considered to be an important lead in RNA-targeting drug discovery. In this study, surface plasmon resonance (SPR) was employed to explore the interaction of aminoglycosides with known tobramycin-binding RNA hairpins (aptamers) and an unrelated RNA hairpin. It was established that aminoglycosides have multiple interactions with RNA hairpins. Unexpectedly, the different hairpins showed comparable affinity for a set of related aminoglycosides. The observed absence of selectivity presents an extra hurdle in the discovery of novel aminoglycosides as specific drugs that target defined RNA hairpins.