  We compute semiclassical corrections to the energy density of kinks in
$\phi^4$ theory and of solitons in the sine-Gordon model in $1+1$ dimensions,
using local and covariant renormalization techniques from quantum field theory
in curved spacetimes. For the semiclassical correction to the energy, we
recover the known results. Our analysis highlights a subtlety in the definition
of a conserved stress tensor for scalar field theories in $1+1$ dimension.
