A stone in the kidney can stay there for years. If it is not infected and not causing any obstruction then it is without symptoms. It may give you a small amount of blood in the urine (often this is only visible under the microscope). If the stone moves into the ureter (the tube from the kidney to the bladder), then its size has an effect on its chance of passing spontaneously. A 4 mm stone has about an 80% chance of spontaneous passage at that point. That does not mean that it will pass quickly or without pain, just that its likelihood of passing is that high. CT scans with narrow "cuts" of 2.5 mm (or less) should be quite sensitive to finding stones and are much more reliable than ultrasounds.
Getting to your procedure, if the urologist cannot locate the stone (maybe it passed silently?) or could not be identified on x-ray because of many technical factors that can influence the study, gas being one of them, then there is essentially nothing to treat. It was definitely in your best interest not to treat what could not be found!
I see no need to treat the stone at this point. I would get a follow-up x-ray of your abdomen (not a CT due to the radiation involved) in another year unless you have an absolute need to know or are planning to travel to places where medical care will not be readily available. If your stone is then found and is growing in size, then I would recommend ESWL as well as a medical workup to determine what to do to stop making stones.
"This information is provided for general medical educational purposes only. It
does not necessarily reflect the opinions of Henry Ford Hospital or the
Vattikuti Urologic Institute. Please consult your physician for diagnostic
and treatment options pertaining to your specific medical condition.”