Fast Backup and Restore of Growing Databases
Concerning PostgreSQL, I can think of two options:

Low level solution:
Use a storage system or a file system that supports snapshots and take a snapshot before the upgrade.
After the test, either discard the snapshot or restore to it.

Database level solution:
Build up a streaming replication standby database and stop replication before you upgrade.
If the test is fine, discard the standby. If the test fails, discard the master database, promote the standby and continue using that.