  In this paper, we study an inverse Steklov problem in a class of
n-dimensional manifolds having the topology of a hollow sphere and equipped
with a warped product metric. Precisely, we aim at studying the continuous
dependence of the warping function dening the warped product with respect to
the Steklov spectrum. We first show that the knowledge of the Steklov spectrum
up to an exponential decreasing error is enough to determine uniquely the
warping function in a neighbourhood of the boundary. Second, when the warping
functions are symmetric with respect to 1/2, we prove a log-type stability
estimate in the inverse Steklov problem. As a last result, we prove a log-type
stability estimate for the corresponding Calder{\'o}n problem.
