Following dupehammer spirit, it looks natural to give them 10-20 see details below extra close votes to bang in their tag. Note how this will also boost dupehammer holders power, allowing them to do their magic 10-20 more times a day.
Another option worth considering is to allow for 10-20 extra close reviews in their tag. Primary purpose of this is promoting use of filtering in reviews (awareness of which still seems to be an issue). But this also takes into account that reviewing in familiar tag is expected to go easier.
A more nuanced breakdown and explanation of the feature (hat tip to Tim Post): 15-20 extra votes (reviews) to silver badge holders, 5 - to bronze...
...perhaps 5 at the bronze level, so people can actually do stuff right away. Then perhaps 15 more at the silver level, which becomes even more useful when you hit gold and unlock the other ability. When folks hit the bronze level, the extra votes will almost always come on the heels of unlocking another privilege just through rep, so this could be a really good way of bringing out even more enthusiasm for that achievement as well.
...perhaps 5 at the bronze level, so people can actually do stuff right away. Then perhaps 15 more at the silver level, which becomes even more useful when you hit gold and unlock the other ability. When folks hit the bronze level, the extra votes will almost always come on the heels of unlocking another privilege just through rep, so this could be a really good way of bringing out even more enthusiasm for that achievement as well.
Worth noting how this is expected to impact smaller sites where typically gold tag badges are too rare for dupehammer to make a significant effect, but silver and bronze ones are more widespread.
A relatively minor (but still, interesting) design challenge for such a feature would be how to handle questions retagged after the vote was cast. Do we keep counting these in "tag quota" or remove from it? Personally I would be inclined to keep - first, because it looks simpler to specify and implement (other way we'd have to handle ugly corner cases, like what if tag was edited out and added back later) and second, because it looks like less prone to complaints ("hey 10 questions in my tag that I voted in the morning were later all retagged and now I am out of votes at all, that's so unfair").
Another interesting challenge would be, how to handle "daily tag limit" data and respective UI for users who have both silver and bronze badges in different tags. (Easy solution for UI would probably be to report amount of "tag close votes" used instead of anbiguousambiguous remaining amount.)
