A memory management unit 22, 34, 48 serves to use first stage of address translation and permission data S1 managed by a guest operating system and second stage of address translation and permission data S2 managed by a hypervisor. If there is a mismatch between the permissions (or other characteristics) provided by these different translation and permission data sets, then a speculative mismatch response is triggered. This speculative mismatch response may comprise storing a virtual address to intermediate physical address mapping within a cache 32, 36 within the memory management unit. Such a cache can subsequently be accessed by an instruction seeking to determine an intermediate physical address associated with a mismatch without having to wait for a full translation (page table walk) operation to be performed.