Isomeric states in 128In and 130In have been studied with the JYFLTRAP Penning trap at the IGISOL facility. By employing state-of-the-art ion manipulation techniques, three different beta-decaying states in 128In and 130In have been separated and their masses measured. JYFLTRAP was also used to select the ions of interest for identification at a post-trap decay spectroscopy station. A new beta-decaying high-spin isomer feeding the isomer in 128Sn has been discovered in 128In at 1797.6(20) keV. Shell-model calculations employing a CD-Bonn potential re-normalized with the perturbative G-matrix approach suggest this new isomer to be a 16⁺ spin-trap isomer. In 130In, the lowest-lying (10⁻) isomeric state at 58.6(82) keV was resolved for the first time using the phase-imaging ion cyclotron resonance technique. The energy difference between the 10⁻ and 1⁻ states in 130In, stemming from parallel/antiparallel coupling of (π0g-19/2) ⊗ (v0h-111/2), has been found to be around 200 keV lower than predicted by the shell model. Precise information on the energies of the excited states determined in this work is crucial for producing new improved effective interactions for the nuclear shell model description of nuclei near 132Sn.