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We investigate in-plane quasiparticle tunneling across thin film grainboundary junctions (GBJs) of the electron-doped cuprateLa$_{2-x}$Ce$_{x}$CuO$_4$ in magnetic fields up to $B=16 $T, perpendicular tothe CuO$_2$ layers. The differential conductance in the superconducting stateshows a zero bias conductance peak (ZBCP) due to zero energy surface Andreevbound states. With increasing temperature $T$, the ZBCP vanishes at thecritical temperature $T_c\approx29 $K if B=0, and at $T=12 $K for B=16 T. Asthe ZBCP is related to the macroscopic phase coherence of the superconductingstate, we argue that the disappearance of the ZBCP at a field $B_{ZBCP}(T)$must occur below the upper critical field $B_{c2}(T)$ of the superconductor. Wefind $B_{ZBCP}(0) \approx 25 $T which is at least a factor of 2.5 higher thanprevious estimates of $B_{c2}(0)$.

Andreev bound states at a cuprate grain boundary junction: A lower bound for the upper critical field