Very generally and at the most basic, you need a precision voltage reference and resistors. Obtaining 0.1% is fairly easy, for resistors it's straightforward, and for voltage references look up "precision voltage reference" (something like this), and bias it with 0.1 to 1 mA.
The actual calibration procedure will vary from meter to meter, so you will need to dig up the appropriate documents.
The display is not the limiting factor (as you point out). Fundamentally, there is a cut-off. If the display was the most expensive part in the meter, then most meters would probably read up to 9999 on all digits. However, there's a couple factors that make the meter ranges what they are.
There is a limit to how high a range goes - the count is a design decision for the meter maker. A 20... meter isn't the only type available either, I personally have a 6000 count meter.
Logarithmically, you get the most bang for your buck by having 2000 counts. See the image of the number line below. By doubling the counts from 1000 to 2000, you get a bigger bang for your buck, and you also get to use one more digit (better for marketing).

There's another reason for not dropping the least significant digit. Part of the gotcha with auto-ranging meters is that you can easily forget that the meter has different measurement ranges, and that the measurement accuracy changes with each range. For example, compare the following displays:
193.00 k
.1930 M
193.0 k <----- Would you notice the missing digit as easily?
Personally, I see it as a more obvious way of conveying information about the measurement. It doesn't detract much from the readability in my opinion.
Best Answer
You can buy a few 0.1% resistors to calculate resistance ranges cheaply.
Voltage is tricker - if you have access to several meters you can 'calibrate by consensus', as it is improbable that they will all go out in the same direction.
Another option is buy a precision voltage reference IC - e.g. AD581 is 10V with 0.1% accuracy.
Current can also be done using voltage across a known, accurate resistance.