[shadowgovt]

In general, such consequences would be applied by the public. If the people feel that the executive overreached and is no longer honoring their oath, the people don't re-elect that executive. There are some exceptions (such as the impeachment power of the federal Congress), but in a system where the public elects the executive, the last recourse of a bad executive is the public's right to elect someone else. And even in cases like the power of congressional impeachment, the punishment they can extend is removal from office and nothing more.

No, if someone broke the law in the process of exercising the executive authority, that's a different issue. But we don't generally have laws of the form "the executive is not allowed to infringe on non-fundamental liberties during an emergency," because history shows that emergencies happen and sometimes people just have to be told what to do (arguably, that's one of the reasons we bother to have an executive at various levels of government).