  We study the Casimir energy of four-dimensional supersymmetric gauge theories
in the context of the rigid limit of new minimal supergravity. Firstly,
revisiting the computation of the localized partition function on $S^1\times
S^3$, we recover the supersymmetric Casimir energy. Secondly, we consider the
same theories in the Hamiltonian formalism on $\mathbb{R}\times S^3$, focussing
on the free limit and including a one-parameter family of background gauge
fields along $\mathbb{R}$. We compute the vacuum expectation value of the
canonical Hamiltonian using zeta function regularization, and show that this
interpolates between the supersymmetric Casimir energy and the ordinary Casimir
energy of a supersymmetric free field theory.
