At the end of the day, you if you can't define success in an objective, measurable way, how can you measure progress towards success or achievement of success?
Subjectively. You don't measure it, you just assess it.
I suppose the clearest example is test exercises like CSTTX or BATUS. There are no clear, measurable numerical standards to hit but there are defined performance criteria against which a battlegroup can be assessed. The key is trusting the assessor to make the right judgement.
Interestingly, this ties in to a point repeatedly made by Stonker about the army spending years looking for the DS solution and punishing creativity. Arguably that's part of a drive for objectivity. Once you look for pure, measurable objectivity, you need a right answer. There's not really any room for saying 'their process was different but it came up with a good result'. Fortunately the army has moved away from the DS solution assement criteria of old towards far more subjective assessments.
An obvious civilian equivalent is marking an academic essay. There are clear performance criteria that can be listed but it's ultimately a judgement call on the part of the marker to work out whether those have been met and to assign a numerical score accordingly. The mechanism for having meaningful results is to train your exam markers appropriately so they generally give similar scores, then moderate their work to ensure quality control. You can then given each student a numerical representation of their performance, but it sure as hell isn't objective.