Before any shutdown is done, I'd advised you to carry out full backups on both applications. Backup the Call Pilot to another network location and depending upon the phone system type, do the same sort of thing.
Another thing I do, if I've not been to the site before is to take photos of all the cabinets and shelf's etc to get a snapshot of the current system status. There is nothing worse than time spent chasing a problem that was already present before the shut down such as a out of service PRI link etc.
It's best to do a controlled shut down on the Call Pilot as this will shut down the services in the correct order.
For the PABX, it depends on the type of system you have. If it's the Option 11 type version, then you should be fine just switching off the power at either the socket or power unit switch.
I always wait until the power has been turned back on for a few minutes, before I would switch on any telephony equipment. I'd let the power settle down first and if you have much IP equipment, then wait until your data switches are on line.
If you have an Option 11 system, then power up the main cabinet first, If possible, have a serial cable connected to TTY 0 to monitor the reboot. I would power up any other cabinets a minute later.
If your call pilot is a built in 2 slot version, then you should see some activity on CDN's after a couple of minutes of it being powered up.
All the best
Firebird Scrambler
Meridian 1 / Succession and BCM / Norstar Programmer in the UK
If it's working, then leave it alone!.