The Cryogenic IR echelle Spectrometer (CRIRES) instrument at the Very Large Telescope (VLT) was in operation from 2006 to 2014. Great strides in characterizing the inner regions of protoplanetary disks were made using CRIRES observations in the L and M band at this time. The upgraded instrument, CRIRES+, became available in 2021 and covers a larger wavelength range simultaneously. Here we present new CRIRES+ Science Verification data of the binary system S Coronae Australis (S CrA). We aim to characterize the upgraded CRIRES+ instrument for disk studies and provide new insight into the gas in the inner disk of the S CrA N and S systems. We analyze the CRIRES+ data taken in all available L- and M-band settings, providing spectral coverage from 2.9 to 5.5um. We detect emission from ^12^CO (v=1-0, v=2-1, and v=3-2), ^13^CO (v=1-0), hydrogen recombination lines, OH, and H_2_O in the S CrA N disk. In the fainter S CrA S system, only the ^12^CO v=1-0 and the hydrogen recombination lines are detected. The ^12^CO v=1-0 emission in S CrA N and S shows two velocity components, a broad component coming from ~0.1au in S CrA N and ~0.03au in S CrA S and a narrow component coming from ~3au in S CrA N and ~5au in S CrA S. We fit local thermodynamic equilibrium slab models to the rotation diagrams of the two S CrA N velocity components and find that they have similar column densities (~8x10^16^-4x10^17^cm^-2^), but that the broad component is coming from a hotter and narrower region. Two filter settings, M4211 and M4368, provide sufficient wavelength coverage for characterizing CO and H_2_O at ~5um, in particular covering low- and high-J lines. CRIRES+ provides spectral coverage and resolution that are crucial complements to low-resolution observations, such as those with JWST, where multiple velocity components cannot be distinguished.