Protection against EMI
This problem has nothing to do with "EMI" in normal electrical engineereng sense. This is a problem with power supplies. 

According to M66 GSM data sheet, the modem needs 1.6 A during transmission phase.



However, according to MP2359 datasheet, the power output is no more than 1.2 A per channel. So your power supply is 50% underrated for the application peak current (while the average is probably met). The internal drop in M66 likely causes it to disconnect from USB, and full modem reboot is needed to function again.

To get some traction, you might need to use HUGE capacitance, maybe 10-20 100uF ceramic caps in parallel on 4.1V rail to alleviate the problem of high peak currents.

P.S. I wonder when posters would start specifying links to datasheets for the involved components, and actually start reading them before posting questions?