Optical clocks represent the most precise experimental devices, finding application in fields spanning from frequency metrology to fundamental physics. Recently, the first highly charged ions (HCI) based optical clock was demonstrated using Ar$^{13+}$, opening up a plethora of novel systems with advantageous atomic properties for high accuracy clocks. While numerous candidate systems have been explored theoretically, the considerable uncertainty of the clock transition frequency for most species poses experimental challenges. Here, we close this gap by exploring quantum logic-inspired experimental search techniques for sub-Hertz clock transitions in HCI confined to a linear Paul trap. These techniques encompass Rabi excitation, an optical dipole force (ODF) approach, and linear continuous sweeping (LCS) and their applicability for different types of HCI. Through our investigation, we provide tools to pave the way for the development of exceptionally precise HCI-based optical clocks.