Superconductivity induced by a magnetic field near metamagnetism is a striking manifestation of magnetically-mediated superconducting pairing. After being observed in itinerant ferromagnets, this phenomenon was recently reported in the orthorhombic paramagnet UTe2. Here we explore the phase diagram of UTe2 under two magnetic-field directions: the hard magnetization axis b, and a direction titled by ≃25-30° from b in the (b,c) plane. Zero-resistivity measurements confirm that superconductivity is established beyond the metamagnetic field Hm in the tilted-field direction. While superconductivity is locked exactly at fields either smaller (for H | | b), or larger (for H tilted by ≃27° from b to c), than Hm, the variations of the Fermi-liquid coefficient in the electrical resistivity and of the residual resistivity are similar for the two field directions. The resemblance of the normal states for the two field directions puts constraints for theoretical models of superconductivity and implies that some subtle ingredients must be in play.