We have studied more than 1000 presolar silicon carbide (SiC) grains from the Murchison CM2 chondrite for C- and Si-isotopic compositions. Twelve SiC X grains, characterized by strong enrichments in 28Si and believed to originate from Type II Supernovae (SNeII), were also measured for Li- and B-isotopic compositions. None of these grains show resolvable isotope anomalies in Li or B. For the seven X grains without Li and B contributions from nearby or attached SiC grains of distinct origins we find on average 7Li/6Li = 11.83 ± 0.29 (solar system: 12.06) and 11B/10B = 4.68 ± 0.31 (solar system: 4.03). The average 7Li/6Li is compatible with the solar system ratio and the lithium in the X grains is likely largely dominated by contaminating Li of laboratory or meteoritic origin. Also, most of the boron in X grains appears to be contamination but the small 11B excess of ~16%, significant at the 2σ level, can be considered a hint for the presence of boron produced by the neutrino process in the parent SNeII. Despite this finding, a quantitative comparison of the B isotope and abundance data of X grains with model predictions reveals deficiencies in our current understanding of the details of B production in SNeII as well as on B chemistry and condensation in SNII ejecta.