We describe an automated method for computing rigorous lower bounds for
topological entropy which was originally introduced in [Day et al., 2008]. We
combine this method with the work of Zin Arai in [Arai, 2007] to find rigorous
lower bounds on topological entropy for 43 hyperbolic plateaus of the H\'enon
map. We also examine 15 area-preserving plateaus and compare our results with
related work.