An exploratory swim is a form of a test swim, but rather than focus on achieving a certain quantity (a certain distance or time), your intention is to attain and sustain a pleasant internal quality, inside your body or inside your mind, and see how far you can go when this is your priority.
There may be some certain distance in your mind that seems to be a limit for how far you can go before certain qualities start to deteriorate beyond your control. It could be 1 length, 200m, 500m, or whatever. This is going to be the only marker you pay attention to.
You select an internal quality that you can already consistently attain under easy conditions.
Now, you will start to swim as gently and silently as you can – as if doing a drill – with the aim of creating that pleasing internal quality. You will resist increasing intensity. Just maintain that easy effort and pace. Only speed up the tempo or intensity if that increases the sense of ease and relaxation.
You want to swim up to that perceived distance limit as gently as you can, more gently than you may have been swimming when you experienced the failures at that point before. And then, if you are maintaining that internal quality, keep on swimming past that limit.
Keep on swimming, and if at any time you start to lose concentration, and therefore start to lose the quality, quickly survey your body for unnecessary tension and effort, and see if you can re-acquire that pleasing internal quality. If you can, keep going as long as the swim is pleasant for you.
If you cannot re-acquire the internal quality, then stop the swim and evaluate how much farther past your perceived limit you just swam. Consider the causes for your success (swimming in a more pleasant state, swimming farther before failure) and the causes of failure (what ultimately disrupted your ability to maintain that quality.