Tests to make sure the migration was successful

In the migration process, how can we test our website after the process to make sure everything has been migrated 100% correctly?
I am not talking about screening by my eye, but several tests to be sure everything is fine and all files and code are migrated.
I am asking as some hosting providers (like Closte, Guru UK, etc.) after the process of migration, says “Complete” with several steps and tests.
I need to provide my clients with something professional. Please advice.