It would seem that amendment has long been ignored. If a state votes to leave the union, it would likely be decided by a federal court as illegal, then go to Supreme Court for them to decide. The problem is that this will take too long, and things will escalate much sooner than they can review the case. For instance: If the people of the state in question refused to pay their taxes to the government they no longer recognize, the feds would attempt to arrest and prosecute. This could very quickly lead to armed conflict, first between those being arrested and the officers of the government, then would expand to include those who support secession. The government would then move to "preserve the union" with the only hammer they own (force) and there we will be. Source: history.
> If a state votes to leave the union, it would likely be decided by a federal court as illegal, then go to Supreme Court for them to decide.
More likely, the declaration would be ignored by the federal government (oh, statements would be made, but no formal action over the declaration.)
OTOH, any action to implement the declaration would be treated as if the declaration had never occurred; if, say, a state decided it's declaration of independence allowed it to seize federal property, interfere with federal agents, etc., well, we've seen that movie before.
If less extreme acts of disobedience with federal laws result from declaration, then those acts will get into court, where (almost certainly) the declaration will again be treated as void and without effect except perhaps as demonstrating adverse intent. Then the state will be forced to escalate or fold.