  We investigate an ultraweak variational formulation for (parameterized)
linear differential-algebraic equations (DAEs) w.r.t. the time variable which
yields an optimally stable system. This is used within a Petrov-Galerkin method
to derive a certified detailed discretization which provides an approximate
solution in an ultraweak setting as well as for model reduction w.r.t. time in
the spirit of the Reduced Basis Method (RBM). A computable sharp error bound is
derived. Numerical experiments are presented that show that this method yields
a significant reduction and can be combined with well-known system theoretic
methods such as Balanced Truncation to reduce the size of the DAE.
