A processor includes a decode unit to decode an instruction that is to indicate a page of a protected container memory, and a storage location outside of the protected container memory. An execution unit, in response to the instruction, is to ensure that there are no writable references to the page of the protected container memory while it has a write protected state. The execution unit is to encrypt a copy of the page of the protected container memory. The execution unit is to store the encrypted copy of the page to the storage location outside of the protected container memory, after it has been ensured that there are no writable references. The execution unit is to leave the page of the protected container memory in the write protected state, which is also valid and readable, after the encrypted copy has been stored to the storage location.