The limitation with multimeters is accuracy, due to the lowest resistance range being usually 0 to 200 ohms. So when we measure a coil, we are right at the very bottom of the measuring range, which is not good for accuracy. IF the multimeter had a 0 to 2 ohms range or even a 0 to 20 ohms range the accuracy would be a lot better.
Below 1 ohm, an atty reader is probably the preferred device, even if its not that accurate, it would still be a lot better than a multimeter IMO.
Further information, not necessary to read, may cause a headache for some readers:
A multimeter is designed to test using minimal test current to avoid damaging components or affecting the circuit it is measuring, that is why they are a high impedance test device, and this is its main limiting factor for reading low ohms. An atty checker on the other hand doesn't care about damaging sensitive electronic components and might push 50mA through a coil to measure the resistance more accurately, whereas a multimeter would pass maybe 1/1000 of that test current (I don't know exact figures).
Another accurate way of checking ohms for DIY type people would be to get a module from ebay that can do constant current (for just a few dollars) and set it for 1 amp using your multimeter's current measure function. Then run the 1 amp current through your coil with alligator clips on the atty posts, and measure the millivolts across the coil with your multimeter. Millivolts will equal milliohms with the 1 amp current flowing. Another application of Ohm's law, V=IR, or in this case, R=V/I.
A cheap atty tester and a $1.50 LED voltage module are what I use most of the time, but a means of testing an atty while its attached to a mod is also occasionally needed and this is where a multimeter comes in handy, or an adaptor with leads coming from the atty reader. A nice DIY modification for an atty reader would be adding 2 banana sockets so you could use multimeter test leads on it. Some of them don't have enough room for the banana sockets though. I think I would like to do this.