  We present our photometric search for potential nuclear star clusters (NSCs)
in ultra-diffuse galaxies (UDGs) as an extension of the SMUDGes catalog. We
identify 325 SMUDGes galaxies with NSCs and, from the 144 with existing
distance estimates, identify 33 NSC hosts as UDGs ($\mu_{0,g}$ $\ge$ 24 mag
arcsec$^{-2}$, $r_e \ge 1.5$ kpc). The SMUDGes with NSCs lie on the galaxy red
sequence, satisfy the NSC-host galaxy stellar mass relationship, have a mean
NSC stellar mass fraction of 0.02 but reach as high as 0.1, have NSCs that are
displaced from the host center with a standard deviation of 0.10$r_e$, and
weakly favor higher density environments. All of these properties are
consistent with previous results from higher surface brightness galaxy samples,
allowing for at most a relatively weak dependence of NSC behavior with host
galaxy surface brightness.
