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Thermal inversions have long been predicted to exist in the atmospheres of ultra-hot Jupiters. However, detection of two species thought to be responsible -- TiO and VO -- remain elusive. We present a search for TiO and VO in the atmosphere of the ultra-hot Jupiter WASP-121b ($T_\textrm{eq} \gtrsim 2400$ K), an exoplanet already known to show water features in its dayside spectrum characteristic of a temperature inversion as well as tentative evidence for VO at low-resolution. We observed its transmission spectrum with UVES/VLT and used the cross-correlation method -- a powerful tool for the unambiguous identification of the presence of atomic and molecular species -- in an effort to detect whether TiO or VO were responsible for the observed temperature inversion. No evidence for the presence of TiO or VO was found at the terminator of WASP-121b. By injecting signals into our data at varying abundance levels, we set rough detection limits of $[\text{VO}] \lesssim -7.9$ and $[\text{TiO}] \lesssim -9.3$. However, these detection limits are largely degenerate with scattering properties and the position of the cloud deck. Our results may suggest that neither TiO or VO are the main drivers of the thermal inversion in WASP-121b, but until a more accurate line list is developed for VO, we cannot conclusively rule out its presence. Future work will search for finding other strong optically-absorbing species that may be responsible for the excess absorption in the red-optical.