1: He had never visited this museum
...would only occur in some "narrative" context that's already set in the past. That's to say it could occur immediately after I met a man yesterday, but not after Do you see that man over there?, for example1.
The Past Perfect form had visited references some time further in the past than the current "reference time" (yesterday, in my first example above). By implication, any "past action" referred to in this way would normally have been "completed" by the (later) "reference time".
But if the action is modified by never, that means it didn't take place at any time, so it's effectively meaningless to think in terms of whether it was completed or not, since it was never even started.
A "present participle" means a continuous (-ing) form (visiting, in this case). When used in a "negating" context involving never, such as...
2: He is never visiting this museum
...our normal understanding is that never means at no time in the future. So it's perfectly possible to append the word again to my second example, which could be said even if he's currently visiting the museum - it's semantically equivalent to He will never visit the museum [again] in the future.
Thus the following two examples mean exactly the same thing, and it's really just a stylistic choice which version to use...
3: We are never giving up.
4: We will never give up.
(At no time in the future are we conceding / will we concede. It ain't gonna happen, ever!)
1 Except if qualified in such a way as to exclude the present time of speaking - as in, for example, That man over there had never visited the museum until today. But even then, many people would find the Present Perfect form has never visited more appropriate.