Methinks both Fredsteer and Urrell are correct. Along with Idleness, Mouldy Paul and Spag. Depending on what sort of remap you want? And how much you want to spend?
What Fredsteer is describing, with car on a rolling road, mapping checked out, tweaks made, performance re-checked through the rev range, more tweaks applied, full rev range recheck for both torque and bhp. Repeat loop till satisfied. Is the "traditional" way of developing a fresh map for an individual car. What I would describe as a "bespoke" re-map. Particularly applicable if not even essential for a car which had been modified or a competition spec engine build with altered cams, bigger turbo, etc. Easily 1-2 hours on a rolling road to get right. Even something as seemingly innocuous as changing from a standard air filter to a K&N can alter the behaviour of the incoming airflow, and so can benefit from a bespoke re-map IF you want to get full benefit from the greater airflow capability. Also applicable to any make and model of car that the re-map specialist is encountering for the first time or "exotica" like supercars, etc. All that rolling road time doesn't come cheap though. Since you are not just paying for a very expensive piece of kit (the rolling road dynamometer), but the time and expertise of the operator in knowing how to interpret the results and how specific mapping tweaks will be likely to affect that particular type of engine. Easy to rack up enough hours on the rollers to accumulate a fairly hefty bill. Still the ideal way to do it though. Fred is 100% correct in that.
The alternative, that I suspect everyone else is thinking of, is what I would describe as an "off the shelf" re-map. Where the remapping company has seen so many of the particular standard/unmodified engine model on their rolling road, that they know exactly what tweaks will work to give a particular performance or economy upgrade. And have stored those away, to be applied as and when needed, next time that engine appears in standard/unmodified tune. No need to put the car through the full rolling road experience. They already know what's gonna work. Just plug the laptop into the car's OBD port. Upload the new map. Unplug laptop. Pay bill. Away you go, 10 mins later. Cost of an off the shelf re-map consequently significantly less than a bespoke job.
"Off the shelf" is the way that the maps for a particular car get applied during its assembly. Based on what works for any particular engine and Receive engine from engine assembly line, insert into bodyshell. Receive ECU from ECU manufacturing plant (not necessarily the same plant or even manufacturer as the engine), with map already built in to suit that engine and car. Plug into car. add fuel and oil. Drive off end of assembly line. Do not pass a rolling road for every car. So the principle of "off the shelf" maps does work. (Unless your name is Aston Martin, where every car built is still tested on a RR before delivery to showroom).
In the case of an off the shelf remap for an existing car, it is essential though that the starting point is the same, fixed set of maps, that the particular re-map set of tweaks was developed for. I.E. the map that the car came off the assembly line using. As that's the one that's the baseline the remapper would have developed the altered map to build on. The "VW dieselgate emissions fix" was another example of an off the shelf remap. Applied by dealers with 10-mins on a laptop. In the scenario though of applying one re-map on top of another, it makes absolute sense to be sure first that the fix has been fully removed before applying a fresh performance/economy map. Unless the re-mapper concerned is confident they have worked on enough "fixed" cars that they have an off the shelf map that achieves both jobs at once.
Two ways to achieve the assurance that the fix has gone cleanly without affecting any other aspect of driveablity. A) An hour on the rolling road (counting 15mins at either end of the running time, getting on/off the rollers with the cooling fans all properly lined up, and the car properly strapped down so it doesn't jump off the rollers at maximum revs in 4th gear, etc.).
Or B) much cheaper: apply the off the shelf "remove fix but retain standard performance" change that most customers want. Drive for a couple of weeks to ensure nothing unexpected has happened. Then come back for a standard performance/economy upgrade off the shelf. With no need to pay extra for a session on the rollers.
That's my "take" on the debate anyway.