In recent years, an increasing number of observational studies have hinted at the presence of warps in protoplanetary discs; however, a general comprehensive description of observational diagnostics of warped discs was missing. We performed a series of 3D smoothed particle hydrodynamic simulations and combined them with 3D radiative transfer calculations to study the observability of warps in circumbinary discs, whose plane is misaligned with respect to the orbital plane of the central binary. Our numerical hydrodynamic simulations confirm previous analytical results on the dependence of the warp structure on the viscosity and the initial misalignment between the binary and the disc. To study the observational signatures of warps, we calculate images in the continuum at near-infrared and submillimetre wavelengths and in the pure rotational transition of CO in the submillimetre. Warped circumbinary discs show surface brightness asymmetry in near-infrared scattered light images as well as in optically thick gas lines at submillimetre wavelengths. The asymmetry is caused by self-shadowing of the disc by the inner warped regions, thus the strength of the asymmetry depends on the strength of the warp. The projected velocity field, derived from line observations, shows characteristic deviations, twists and a change in the slope of the rotation curve, from that of an unperturbed disc. In extreme cases even the direction of rotation appears to change in the disc inwards of a characteristic radius. The strength of the kinematical signatures of warps decreases with increasing inclination. The strength of all warp signatures decreases with decreasing viscosity.