There are many and these will depend on what you want to measure and how you are defining quality.
The same will go with the tools associated with this measurement. A bit more information and we may be able supply more focussed guidance.
I'd say you get your "customer" to write the metrics, tell you what they want then compare to see how well you meet their requirements, not just at the end but at frequent "sanity checks" or stage reviews during development. Depends on them knowing what they want of course, and giving you sufficient detail to make it happen.
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I would say that is a pipe dream. The best metrics in the world can't ensure anything! They can help by displaying the results of what has been done and help to predict the outcome of a project, if, and only if, they are used properly.
Too many metrics can also muddy the waters.