Rather than sticking around in the platform she was given when she came in through the rift (the Forerunner Monitor-esque bulb thing), Cortana opted to hand the platform over to Emily and integrate with his armor. This leaves the two very closely connected and makes Emile that much more dangerous with Cortana handling all of his armor's systems and feeding him intel and assistance in battle.

Besides speaking with Washington, she used her holo-projection to talk to a few people herself, such as EDI and Washington. Mostly about tanks. When Emile went to speak to Shepard, she listened in, contributing with explanations on UNSC tech on the like when she had the opportunity.

At some point, she would've offered her mastery at hacking and encryption to Shepard in whatever capacity it could help.