Boron-rich materials combine chemical stability with refractory properties and, consequently, are interesting for high-temperature thermoelectric applications. Therefore, the magnetic, electrical, and thermal transport properties of the ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CrB}}_{4}$ series have been investigated here to employ the concept of correlation-enhanced thermoelectric properties. Combining x-ray diffraction and energy- or wavelength-dispersive spectrometry, we find a rather narrow stability range of ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CrB}}_{4}$, only samples on the Y- and Ce-rich substitution limits $(x=0,\phantom{\rule{0.28em}{0ex}}0.05,\phantom{\rule{0.28em}{0ex}}0.95,\phantom{\rule{0.28em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}1)$ were obtained. Electrical resistivity data show a change from semiconducting $(x=0)$ to metallic behavior upon Ce substitution $(x\ensuremath{\ge}0.95)$. From magnetic susceptibility measurements and x-ray absorption spectroscopy, we find a temperature-dependent intermediate valence state of Ce of about $+3.5$. However, a fit of the magnetic susceptibility data to the Coqblin-Schrieffer model yields a surprisingly high Kondo temperature of about 1100 K. Together with the good thermal conductivity for the studied substitution series this impedes a suitable thermoelectric performance. Electronic structure calculations for ${\mathrm{YCrB}}_{4}$ support its narrow gap semiconducting nature in contrast to previous studies. Surprisingly, its electronic structure is characterized by pronounced van Hove singularities very close to the Fermi-level ${E}_{\mathrm{F}}$. They originate from nearly dispersionless Cr $3{d}_{{z}^{2}\ensuremath{-}{r}^{2}}$-derived bands in a large part of the Brillouin zone, suggesting the appearance of electronic instabilities upon rather small electron doping into these states.