Probably nothing you've not already figured out. You could get some coarse grain metrics using a batch file to coordinate:
- start monitoring
- copy file
- stop monitoring
Copy file might just be initiating a file copy between two nodes on the LAN, or it might initiate a FTP copy between two nodes on the WAN.
Monitoring could be as basic as writing the current time to output or file, or it could be as complex as adding performance counter metrics from the network adapter on the two machines.
A commercial WAN emulator would also give you the information your looking for. I've used the Shunra Appliance successfully in the past. Its pretty expensive, so I'd really only recommend it if critical business success is riding on understanding how application behavior could change based on network conditions and is something you could incorporate into regular testing activities.