We describe a new design and experimental technique for point-contact spectroscopy in non-destructive pulsed magnetic fields up to 70 T. Point-contact spectroscopy uses a quasi-dc four-point measurement of the current and voltage across a spear-anvil point-contact. The contact resistance could be adjusted over three orders of magnitude by a built-in fine pitch threaded screw. The first measurements using this set-up were performed on both single-crystalline and exfoliated graphite samples in a 150ms, pulse length 70 T coil at 4.2K and reproduced the well known point-contact spectrum of graphite and showed evidence for a developing high field excitation above 35 T, the onset field of the charge-density wave instability in graphite.