Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly charged ions (HCIs) made HCIs accessible for high-resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore a possibility to develop optical clocks using transitions between the ground and a low-lying excited state in Cf15+ and Cf17+ ions. Using a high-accuracy relativistic method of calculation, we predicted the wavelengths of clock transitions, calculated relevant atomic properties, and analyzed a number of systematic effects (such as the electric quadrupole, micromotion, and quadratic Zeeman shifts of the clock transitions) that affect the accuracy and stability of the optical clocks. We also calculated magnetic dipole hyperfine-structure constants of the clock states and the blackbody radiation shifts of the clock transitions.