  Experimental evidence for the existence of a fluctuating charge-density wave
order in the pseudogap regime of YBa$_2$Cu$_3$O$_{6+x}$ has renewed interest in
its interplay with superconductivity. Here, we consider the problem within a
nonlinear sigma model, which was recently proposed to describe the apparent
competition between the two order parameters. In particular, we use a
saddle-point approximation to calculate the properties of superconducting
vortex excitations within such a model. In addition, we analytically calculate
a collection of experimentally observable quantities, which probe both the
superconducting and charge-density wave fluctuations, and identify expected
signatures of thermally excited vortices.
