  Recently, a theory for the tropicalization of a spherical homogeneous space
$G/H$ was developed by Tassos Vogiannou. We extend his ideas to define the
tropicalization of a spherical $G/H$-embedding. This generalizes the
construction of tropicalization of toric varieties. We also extend an alternate
definition of spherical tropicalization via Gr\"obner theory developed by
Kiumars Kaveh and Christopher Manon and show that the two notions of extended
tropicalization coincide.
