  Discovering new actively-accreting protoplanets is crucial to answering open
questions about planet formation. However, identifying such planets at orbital
distances where they are expected to be abundant is extremely challenging, both
due to the technical requirements and large distances to star-forming regions.
Here we use the kernel phase interferometry (KPI) technique to search for
companions around the $\sim$6 and $\sim$8 Myr old Herbig Ae stars MWC 758 and
MWC 480. KPI is a data analysis technique which is sensitive to moderate
asymmetries, arising from eg. a circumstellar disk or companions with contrasts
of up to 6-8 mags, at separations down to and even below the classical Rayleigh
diffraction limit ($\sim 1.2\lambda / D$). Using the high spectral resolution
K-band mode of the SCExAO/CHARIS integral field spectrograph, we search for
both excess Br-$\gamma$ line emission and continuum emission from companions
around MWC 480 and MWC 758. We are able to set limits on the presence of
rapidly accreting protoplanets and brown dwarfs between 4 and 16 au, well
interior to those of previous studies. In Br-$\gamma$, we set limits on excess
line emission equivalent to accretion rates ranging from $10^{-5}
M_{j}^{2}.yr^{-1}$ to $10^{-6}M_{j}^{2}.yr^{-1}$. Our achievable contrasts
demonstrate that KPI using SCExAO/CHARIS is a promising technique to search for
giant accreting protoplanets at smaller separations compared to conventional
imaging.
