As you already know, this is a controversial subject. Sometimes, on matters like these, we have to attempt to understand the teaching of scripture the best we can without giving an absolute yes or no. First of all, there is certainly nothing directly stating that a woman cannot say amen. Therefore, we have to look at scriptures and try to apply them the best we can.
The context of 1 Corinthians 14:34 certainly deals with speaking in tongues. However, it must also apply to other examples of speaking out as well since the next verse states: "And if they will learn any thing, let them ask their husbands at home: for it is a shame for women to speak in the church." Speaking in tongues was never a way to find out things in church. This must involve more. The passage had been dealing with the problem of everyone speaking out at once in their attempts to take over the service. Verse 26 states, "How is it then, brethren? when ye come together, every one of you hath a psalm, hath a doctrine, hath a tongue, hath a revelation, hath an interpretation. Let all things be done unto edifying."
That is, everyone was trying to speak out at once and they were in the process creating a church service that was a mass of confusion. Paul states that God is not the author of confusion (v.33) and that the church should be operated "decently and in order" (v.40). In order to achieve this, he set up several rules for their services. He limited the number who spoke to two or three; required them to speak in turn; and limited the speaking to men. When taken in this context, the command for women to ask their husbands any questions at home makes more sense. Evidently, women who did not understand something were just speaking out loud during the service and questioning what the preacher had just said. As you can imagine, this made it very difficult for the preacher to preach as God intended him to do.
Now, as you can see, there is still nothing here that absolutely rules out a woman saying amen to something the preacher says. But there are some other considerations. The biblical picture of a godly woman seems to be one who does not assert herself. I know that the feminists would have a fit with this, but the least of their concerns is to be godly. The trouble is, many women in churches today have the same philosophy as the world and just do not know it. Let us consider some of the biblical descriptions of a godly woman.
- Shamefacedness (1 Timothy 2:9). This is simply the opposite of a glaring, proud look. Jeremiah 3:3 speaks of one who has a "whore's forehead" and "refusedst to be ashamed." The godly woman will blush at abominations; the ungodly are unable to blush (Jeremiah 6:15; 8:12). This comes from her continual exposure to sin and perversion. She loses her ability to blush.
- Sobriety (1 Timothy 2:9, 15). This indicates a seriousness. She is to have a self-control about her nature. She is not to be flighty or flirty.
- Subjection (1 Timothy 2:11-12). Here, it is connected with not usurping authority over the man and being "in silence." Earlier in this chapter, Paul refers to public prayer and here to teaching. He is obviously dealing with ministry and worship in the church. Loud and aggressive amens would probably not match this picture of a godly woman. In 1 Peter 3:1, being in subjection to a lost husband is given as the best way to win him to Christ "without the word." The one in subjection usually allows the other to speak first.
- Meek (1 Peter 3:4). She is to have a meek and quiet spirit. To be meek means to be mild and gentle.
- Quiet (1 Peter 3:4). She is to have a quiet spirit. This does not mean that a Christian lady cannot speak. However, it means that she displays an inner strength without an outward forwardness.
Some will look at these verses and the qualities of a godly woman and will conclude that loud displays in worship are not appropriate for Christian ladies. I tend to agree with them. However, quietly amening a statement or nodding the head are certainly not loud displays. Others will point out that there is no command that women not shout amen and I have to admit that this is true though I cannot see how this matches with the biblical description of a Christian lady. In the end, I believe this is one thing that is partly decided by the convictions of the person and partly by the practice of the individual church. I know that this is not an absolute answer, but I hope it helps you think the problem through in a biblical matter. Thank you for the question.