Author Institution: JILA, National Institute of Standards and Technology and University of Colorado Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USAThe JILA electron electric dipole moment (eEDM) experiment will use a low-lying, metastable 3Ξ1β state in trapped molecular ions of HfF+ or ThF+. Prior to this work, the low-lying states of these molecules had been investigated by PFI-ZEKE spectroscopy. However, there were no detailed studies of the electronic structure. The recently developed technique of frequency comb velocity modulation spectroscopy (VMS) provides broad-bandwidth, high-resolution, ion-sensitive spectroscopy, allowing the acquisition of 150 cmβ1 of continuous spectra in 30 minutes over 1500 simultaneous channels. By supplementing this technique with cw-laser VMS, we have investigated the electronic structure of HfF+ in the frequency range of 9950 to 14600 cmβ1, accurately fitting and assigning 16 rovibronic transitions involving 8 different electronic states including the X1Ξ£+ and a3Ξ1β states. In addition, an observed 3Ξ 0+β state with coupling to both the X and a states has been used in the actual eEDM experiment to coherently transfer population from the rovibronic ground state of HfF+ to the eEDM science state. Furthermore, we report on current efforts of applying frequency comb VMS at 700 - 900 nm to the study of ThF+, which has a lower energy 3Ξ1β state and a greater effective electric field, and will provide increased sensitivity for a measurement of the eEDM