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The black mace states that if it causes a wound, a toughness test is to be taken. The following questions I have about the mace are:

1) If the black mace causes multiple wounds, does it cause multiple toughness tests on the same model? I.E. Wounding a 3 wound model twice.
2) Is there one or two separate toughness tests that are to be taken per round of combat? I.E. Test when the wounds are caused, and at the end of the assault phase.

This came up in a game I played today, and it didn't quite make sense, as my opponent was telling me I was required to take a toughness test per wound, and again at combat resolution, all against the same model. Clarification?

1) Yes, and you resolve each wound separately - so roll to save (if anything), if failed toughness test, if passed roll save for 2nd wound, etc
2) two - the first is "fail = death" one at end of phase means you just take a wound if you fail.

Multiple wounds leading to multiple tests:
The key word to look at in the rules is 'immediately.' Whenever you encounter this word in any rule, you need to stop whatever you are doing and resolve what the rule is telling you to immediately resolve. Should that order of event create a situation where you might suffer from multiple characteristic tests then you are forced to endure multiple characteristic tests. There is nothing that I can easily find which limits characteristic tests to one per turn/phase, but I might of overlooked something here. If not, then you do not have any grounds to ignore the second, third or even more toughness tests that might be called for.

In this case as soon as you fail a saving thrown on the wound, you must take a toughness test. These tests are not carried out at the end of the phase, I will go into that below in more detail, but immediately on suffering an unsaved wound. Only after that test is resolved do you continue to allocate wounds, either to the model in question if it passed to the next target down the line. If these additional wounds are also unsaved, then you have met the requirements for the clause telling you to carry out a toughness test. It is irrelevant if any tests have been carried out in the past, even in that same phase, as that does not make you immune to these additional tests.

Test at the end of the phase:
This one is a bit more tricky but not because of the order of events. The order of events is pretty clear, at the end of any phase which X has happened models within Y distance carry out a toughness test. Sorry about the X and Y markers, but this is going a little to close to outright stating what the rule does and I do not do that sort of thing here due to copy write reasons. In any case, if the requirements for this additional rule have been met then this part of the rule is also followed regardless of any tests you might of carried out prior. Do keep in mind that this additional rule, unlike the immediate one above, is only ever carried out once and not multiple time for each individual wound created.

Now to get onto the part that makes this tricky as there are situations where you might end up making just one toughness test and completely ignoring the 'additional test' called for in the rules.

There are two exception clauses within the section informing you which models take the additional toughness test. One of these exceptions is any model which has suffered an unsaved wound from the black mace during that phase. Should you only have a single model in base contact with the mace bearer, and no other model within the before mentioned Y distance, then you do not need to make the additional toughness test. The only model which could be affected by this additional test has already suffered a wound from the mace and is therefore immune to the additional test which is carried out at the end of the phase.

So do keep that little clause in mind when you fight a model wielding the black mace. Keep other units back Y inches and engage with a single model. Though to be honest, the best advice you can receive is to destroy the mace carrier at range and never engage in close combat to begin with. It is an expensive little piece of war gear but for a reason, it is one of the most powerful close combat weapons that can ever be fielded. It's pseudo-instant death gets around all sorts of things designed to prevent just that and it can even destroy models not actually engaged in the combat, such as those simply watching from the side line or unfortunate enough to be within spitting distance of the mace bearer during said combat.