Tim, Looking at the QRH, there is a full page of information and procedures to follow after the loss of AP, in flight.
First, go to the instrument source select switch and select ALTN.
Place both pilots' HSI range selectors in same position
If left FMC failed, select Right AP or center. Leave Vnav on to have AT.
Some notes about ATC.....

If both FMC fail, it becomes Complete FMC Failure.

In that case, use VOR, DME and ADF , Radar to navigate on raw data.
Plot and do position update as needed to maintain correct ground track.
If this fail, ask ATC for DF steer
Use heading select mode and raw data on HSI display.

The B757 is one of the most reliable and safest plane. Mine is anyway !

Happy Flying !   8-)

Raymond    Boeing or nothing
KFLL     South Florida