Series resistors (around 22 to 100 ohms often) damp reflections/ringing on fast logic and thus stop double-clocking which can cuase malfunctioning, particularly for clock signals - they are not doing a lot for EMI though. Think of this as like damping a mechanical resonance. For really fast signals matched termination is used which prevents resonance and reflections very effectively without any bandwidth limiting - however this is typically power hungry.
Many CMOS logic chips can produce 2 to 5ns rise/fall times, which if being used for a serial output at 115200 baud is complete overkill as rise/fall of 500ns would be completely adequate. Adding a small series resistor here doesn't really do anything as serial signals / UARTs are inherently immune to double-clocking, though you could use larger R values and have an explicit RC filter, such as 1k / 470pF in this case.
To reduce EMI significantly you typically filter with ferrites and capacitors to slow the edges down a whole lot more (think like adding mechanical mass to slow down movement). However if the signal has to be fast you can't do that so much (unless its a differential signal where you can add a common-mode choke to reduce common-mode EMI). Using lower voltage also reduces EMI (and power), such as LVDS signals, commonly used where high baud rates are a requirement (100's of Mbaud)
Many chips designed to drive digital busses have control over rise/fall times, or are available in slower versions for use with slower busses. For instance you can get RS485 drivers at a range of top speeds.
The typical networks for sending a digital signal from one board to another involve EMI filtering at the sending end, rail-clamping protection diodes and more EMI filtering at the receiving end. Differential signalling is preferrable if you can afford the extra connections, especially with twisted-pair cabling.
You can model the EMI filters in Spice to get a feel for their behaviour (rather than just guess). The tricky part is knowing which signals will be the most problematical, as this depends on many factors, cable length and type, baud rate, voltage, singleded/differential, current levels, spectrum of the signal...
However EMI is also a problem on the power supply wiring, and much bigger filters are needed to reduce this as there are significant currents involved. Again ferrites and capacitors are typically used.