Wait a few more days, if they still don't hatch they are duds (infertile or DIS).

Then, remove the nest entirety to give the pair a break before breeding them again.

I have a pair of star finches in my outdoor aviary that have been sitting on eggs now for 16 days without any sign of them hatching. I can't actually see into the nest without disturbing the birds because of where it is in the aviary. The birds haven't left the eggs for the whole of the sixteen days so I don't know what has happened. Should I wait a few more days or just remove the nest? All help is much appreciated!