You'd typically spec a metrology room to hold 68 +/-XX NON CONDENSING. Using an undersized system might produce the 68* but with 90 to 100% relative humidity. A good example of this is a house or commercial building with an undersized system. It doesn't feel hot, but it feels sorta clammy.
To control the humidity you have to run the cooling coil at some temperature substantially less than the space temperature. Chilled water systems typically hold the water temp at 45*F and the discharge air temperature coming off the cooling coil will be in the 50* range. At 50 the air is saturated, but as it warms by mixing with air in the space its capacity to hold moisture increases and its relative humidity decreases. Direct expansion type cooling coils run in the 40* range and the discharge air is still around 50* for normal applications.
Obviously you can't just keep driving the temp down to control humidity, so its normal to have either reheat capability downstream or have the ability to mix warm and cold air in either a hot deck / cold deck air handler or in mixing boxes that are fed with both hot and cold air. Either of these modulate to provide more cool air and less warm as the temp moves above the setpoint, and further modulate to maintain a balance of hot/cold that maintains the space conditions when the temp is at the setpoint.
We had a couple large package heat pumps on the shop at Michelin. The units had an economizer on them, which is a damper setup that will pump outside air into the building for cooling purposes if the outdoor temp is cool enough. The cooling would run all day and then at sometime near dark the outdoor temp would drop enough to kick in the economizer. Problem was, the outdoor air was near saturation as it typically is about the time things begin to cool down in the evening. Moisture would condense on the surface plate in particular, and if anything was left sitting on it we'd have to bump it before we could move it due to rust starting to form. Supposedly an economizer has an enthalpy based control which is reading both temperature and humidity, but we found the ones on our units were evidently illiterate
The only solution we found that really worked reliably was to disable the economizers and let the mechanical cooling run as necessary.
Note to OX... The a/c compressor runs with the defroster to do the same thing as I described above. The cooling coil knocks the water out of the air and then the heater core heats it back up so you're blowing warm dry air onto the windshield. If its real cold outside the humidity will be low enough that just heating the air is a plenty, but if its about 50 to 60 outside and raining and dew wants to form on the inside of the windshield, the defroster will have a hard time getting the dew to evaporate without the a/c being able to run. I seldom turn the cooling on in my truck in the summer, but when the low pressure switch went bad and locked out the compressor I had to replace it to allow the compressor to run because the windshield would fog up and the defroster wouldn't do a thing but make it worse.