  We study the applicability of the covariant holographic entanglement entropy
proposal to asymptotically warped AdS$_3$ spacetimes with an SL(2,R) x U(1)
isometry. We begin by applying the proposal to locally AdS$_3$ backgrounds
which are written as a real-line fibration over AdS$_2$. We then perturb away
from this geometry by considering a warping parameter $a=1+\delta$ to get an
asymptotically warped AdS$_3$ spacetime and compute the dual entanglement
entropy perturbatively in $\delta$. We find that for large separation in the
fiber coordinate, the entanglement entropy can be computed to all orders in
$\delta$ and takes the universal form appropriate for two-dimensional 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 two-dimensional CFT
answers, with the left-moving and right-moving temperatures appearing
appropriately in the result.
