To be clear, you're simply exceeding the range of the higher resolution mV scale provided by the meters.
In the case of the UT61E, that limit is stated to be 220mV, resolution 0.01 mV, in the manual (findable online if you've lost yours). On the V setting, when the reading is under 2.2V resolution is 0.0001V (0.1 mV).
The answer is don't use the mV scale for this case. Read the V scale. Convert to mV if you want.
0.6038V = 603.8 mV
I didn't look up the numbers for your fluke, but it's presumably a range issue there as well.