The holographic dictionary for spacetimes which are not asymptotically AdS remains elusive. I will present evidence for the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS3 spacetimes, which have SL(2,R) x U(1) isometry and are relevant in the study of astrophysical black holes. I will begin by applying the covariant proposal to locally AdS3 backgrounds which are written as a real-line fibration over AdS2. A "small" perturbation of this geometry gives warped AdS3, and I will calculate the dual entanglement entropy perturbatively in this case. For large separation in the fiber coordinate, we will see that the entanglement entropy can be computed to all orders in the perturbation and only then takes the universal form appropriate for 2D CFTs. The warping-dependent central charge thus identified exactly agrees with previous calculations in the literature. Performing the same perturbative calculations for the warped BTZ black hole again gives universal 2D CFT answers at finite temperature, with the left-moving and right-moving temperatures of the warped BTZ black hole appearing appropriately in the result.