Can you explain a little more about what you are doing? The sep funnel does work with bases, but it is better used for acid washes. For acid washes you put your filtered NP solvent into the sep funnel, then add acid water several times to wash the good stuff out of the solvent. Assuming your basic solution contains the goods, I'm not sure how you are supposed to be washing the NP solvent with more base liquid, that seems to be defeating the purpose. I've heard of people using sep funnels to collect NP solvent off an STB, but it seems to me that sucking it off the top is a lot less work.
If you are doing a sodium carbonate wash trying to clean the solvent, you might lose a little, but it supposedly works. I don't bother, personally.
In any case, what I do to break emulsions in a sep funnel is to wrap the funnel with a hot rag. Wet a rag and heat it in the microwave a minute or so to get it hot enough so it is hard to handle, but not so much it dries out and catches fire. It might need to be heated several times to warm up everything in the funnel, but it works. I've also heard of people submerging the whole thing in hot water, or on its side, but that would be messy.