The “Planetary Instrument for X-ray Lithochemistry” (PIXL) X-ray spectrometer conducts in situ geochemical analyses of martian rocks and regolith interrogated by the Mars 2020 rover, Perseverance. In addition to quantifying primary rock-forming elements, PIXL can quantify trace elements that in turn can provide additional constraints on the geologic history of Mars. Accurate quantifications of trace elements can require additional analytical techniques to mitigate experimental, background, and crystalline effects within PIXL spectra. In this study, we focus on reducing the impact of these effects and investigate the potential presence of rare earth elements (REEs). The study specifically investigates cerium given its typical relative abundance in many geologic materials compared to other REEs and its potential to mimic fluorescence features produced by organics under deep UV excitation. A detailed analysis of PIXL targets analyzed through the first 887 martian days of the Perseverance mission did not produce any conclusive Ce detections. Phosphorus-enriched materials analyzed by PIXL are estimated to contain sub-675 ppm Ce and sulfate-enriched materials sub-450 ppm Ce. The method presented can help constrain limits on the abundance of additional trace elements of interest that also face a similar analytical burden. PIXL's potential to assess REE abundances, outside of yttrium, is limited for expected concentrations in surface materials. Determining most REE concentrations in materials interrogated by Perseverance will therefore likely require terrestrial analyses.