  We derive expressions for the local ideal magnetohydrodynamic (MHD) equations
for a warped astrophysical disc using a warped shearing box formalism. A
perturbation expansion of these equations to first order in the warping
amplitude leads to a linear theory for the internal local structure of
magnetised warped discs in the absence of MRI turbulence. In the special case
of an external magnetic field oriented normal to the disc surface these
equations are solved semi-analytically via a spectral method. The relatively
rapid warp propagation of low-viscosity Keplerian hydrodynamic warped discs is
diminished by the presence of a magnetic field. The magnetic tension adds a
stiffness to the epicyclic oscillations, detuning the natural frequency from
the orbital frequency and thereby removing the resonant forcing of epicyclic
modes characteristic of hydrodynamic warped discs. In contrast to a single
hydrodynamic resonance we find a series of Alfv\'{e}nic-epicyclic modes which
may be resonantly forced by the warped geometry at critical values of the
orbital shear rate $q$ and magnetic field strength. At these critical points
large internal torques are generated and anomalously rapid warp propagation
occurs. As our treatment omits MRI turbulence, these results are of greatest
applicability to strongly magnetised discs.
