There is a recent session at the Desiring God Conference 2013 where the speaker Tope Koleoso attempts to argue for his case that Reformed people should be Charismatics. The Cripplegate has analyzed his talk (Part 1, 2, 3), while Dr. R Sott Clark has responded to it from a historical point of view.
Perhaps the greatest issue that irks me about all these Charismatic arguments is that almost all of them totally misrepresent the opposing side. To disagree with Cessationism is one thing; to misrepresent it is another. I admit my still limited exposure to Charismatics, but I have not yet found one Charismatic who has adequately represented the Cessationist argument in its strongest form, and then show why he rejects it. Instead, we are treated to trite nonsense like "Cessationists fear the Holy Spirit." If I want to be polemical, I could very well state that Charismatics like Koleoso probably believes in a different Spirit than the one I and other cessationists believe in, because his description of the Holy Spirit certainly does not seem like the person I see described in the Scriptures. So I could very well counter that cessationists do not fear the Holy Spirit; we just fear that the Spirit Koleoso described is not the Holy Spirit at all.
There are many reasons why Reformed Christianity is antithetical to Charismatism, reasons which I cannot do justice to in this short post. My main contention has always been that Reformed Christianity believes in Sola Scriptura, particularly its teaching on the sufficiency of Scripture and thus the sufficiency of the means of grace ordained in God's Word for our growth in Chris, while Charismatism in every form denies this to some extent. In Charismatism, Scripture is not sufficient for the Christian life, for extra revelation of some sort (e.g. prophecy, word of knowledge, interpreted tongues) is necessary for the Christian life. Granted, reformed Charismatics do not consider such revelations on the same level as Scripture, but still they are considered necessary for the Christian life in some sense. In practice, the ordinary means of grace are deemed to be insufficient for the Christian walk. Rather, Charismatism must in some sense add practices like receiving "word of prophecy," "speaking in tongues," "dreams," "vision" etc as being needed for the Christian walk, even if they are needed merely to "enhance" one's spiritual walk. Charismatism therefore has a denial of the fullness of Sola Scriptura inherent within it. They could very well hold to parts of Sola Scriptura or even most of it, but in the final analysis they must depart from the Reformation slogan of Sola Scriptura, or cease being Charismatic in any real sense of the term.
There is thus no way for Reformed Christians to be Charismatics, for there is a fundamental difference between the two beliefs. Reformed Christianity cannot be reduced to the TULIP or the 5 points of Calvinism, for Reformed Christianity is not just Reformed Soteriology, but rather Reformed Christianity has its own pneumatology which is diametrically opposed to the pneumatology of the Charismatics. Koleoso's call therefore only makes sense in the shallow waters of New Evangelicalism, where doctrines are disjointed and not seen holistically.
There are Reformed, and there are Charismatics. There are 'reformed' Charismatics, but there will never be Reformed Charismatics. The whole term itself is an oxymoron, not even historically, as Dr. Clark points out, but doctrinally and logically. One might as well speak of a Oneness Pentecostal Trinitarian, or an Arian Modalist, all of which do not exist in the same logical sense that square circles don't exist.
Perhaps the day will come when 'reformed' Charismatics will stop having Charismatic altar calls. Perhaps the day will come when Continuationalists will finally adequately represent the Reformed objection to their position. But I'm not holding my breath for any of that to happen.
[See also: This is why Charismatics are simply not Reformed]