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Fairly often. One strategy I've seen is to compare meta-analyses to a later very-large study (rare for obvious reasons when dealing with RCTs) and seeing how often the confidence interval is blown; usually much higher than it should be. (The idea is that the larger study will give a higher-precision result which is a 'ground truth' or oracle for the meta-analysis's estimate, and if it's later, it will not have been included in the meta-analysis and also cannot have led the meta-analysts into Milliken-style distorting their results to get the 'right' answer.)
For example: LeLorier J, Gregoire G, Benhaddad A, Lapierre J, Derderian F. "Discrepancies between meta-analyses and subsequent large randomized, controlled trials". N Engl J Med 1997;337:536e42
(You can probably dig up more results looking through reverse citations of that paper, since it seems to be the originator of this criticism. And also, although I disagree with a lot of it, "Combining heterogenous studies using the random-effects model is a mistake and leads to inconclusive meta-analyses", Al khalaf et al 2010.)
I'm not sure how much to trust these meta-meta analyses. If only someone would aggregate them and test their accuracy against a control.