A processor comprising: a decode unit to decode an instruction of an instruction set of the processor, the instruction to support live migration of a protected container indicating a page of a protected container memory, and indicating a storage location outside of the protected container memory; and an execution unit coupled with the decode unit, the execution unit, in response to the instruction, to: write protect the page of the protected container memory; flush writable permissions for the page of the protected container memory cached in the processor; encrypt a copy of the page of the protected container memory; store the encrypted copy of the page to the indicated storage location outside of the protected container memory, after it has been ensured that there are no writable references to the page of the protected container memory; and leave the page of the protected container memory in the write protected but valid and readable state after the encrypted copy of the page has been stored to the indicated storage location outside of the protected container memory, wherein to flush writable permissions for the page includes the execution unit, in response to the instruction, to flush all translations from a virtual to physical address for the page of the protected container memory from all translation lookaside buffers of the processor, wherein the execution unit, in response to the instruction, is to: detect an attempted write to the write protected page of the protected container memory; write unprotect the page of the protected container memory; and invalidate the encrypted copy of the page stored in the storage location that is outside of the protected container memory. a decode unit to decode an instruction of an instruction set of the processor, the instruction to support live migration of a protected container indicating a page of a protected container memory, and indicating a storage location outside of the protected container memory; and an execution unit coupled with the decode unit, the execution unit, in response to the instruction, to: write protect the page of the protected container memory; flush writable permissions for the page of the protected container memory cached in the processor; encrypt a copy of the page of the protected container memory; store the encrypted copy of the page to the indicated storage location outside of the protected container memory, after it has been ensured that there are no writable references to the page of the protected container memory; and leave the page of the protected container memory in the write protected but valid and readable state after the encrypted copy of the page has been stored to the indicated storage location outside of the protected container memory, write protect the page of the protected container memory; flush writable permissions for the page of the protected container memory cached in the processor; encrypt a copy of the page of the protected container memory; store the encrypted copy of the page to the indicated storage location outside of the protected container memory, after it has been ensured that there are no writable references to the page of the protected container memory; and leave the page of the protected container memory in the write protected but valid and readable state after the encrypted copy of the page has been stored to the indicated storage location outside of the protected container memory, wherein to flush writable permissions for the page includes the execution unit, in response to the instruction, to flush all translations from a virtual to physical address for the page of the protected container memory from all translation lookaside buffers of the processor, wherein the execution unit, in response to the instruction, is to: detect an attempted write to the write protected page of the protected container memory; write unprotect the page of the protected container memory; and invalidate the encrypted copy of the page stored in the storage location that is outside of the protected container memory. detect an attempted write to the write protected page of the protected container memory; write unprotect the page of the protected container memory; and invalidate the encrypted copy of the page stored in the storage location that is outside of the protected container memory.