A dense forest of slender bright fibrils near a small solar active region is seen in high-quality narrowband Ca II H images from the SuFI instrument onboard the Sunrise balloon-borne solar observatory. The orientation of these slender Ca II H fibrils (SCF) overlaps with the magnetic field configuration in the low solar chromosphere derived by magnetostatic extrapolation of the photospheric field observed with Sunrise/IMaX and SDO/HMI. In addition, many observed SCFs are qualitatively aligned with small-scale loops computed from a novel inversion approach based on best-fit numerical MHD simulation. Such loops are organized in canopy-like arches over quiet areas that differ in height depending on the field strength near their roots.