  We investigate dense output formulae (also known as continuous extensions)
for strong stability preserving (SSP) Runge-Kutta methods. We require that the
dense output formula also possess the SSP property, ideally under the same
step-size restriction as the method itself. A general recipe for first-order
SSP dense output formulae for SSP methods is given, and second-order dense
output formulae for several optimal SSP methods are developed. It is shown that
SSP dense output formulae of order 3 and higher do not exist, and that in any
method possessing a second-order SSP dense output, the coefficient matrix A has
a zero row.
