I agree with SeaJambon and Sarah that canning mushrooms are dangerous. Here, you can buy enoki mushrooms in a soy sauce bottled, and shiitake mushrooms in a thick soy sauce which needs refrigeration. That means you need an excellent recipe.

I've also tried drying but I think its too hot outside now, so will develop fungus. Freezing, then making your sauce after defrosting is probably your best bet. But i usually don't have so many mushrooms left over--used up!

SeaJambon is absolutely right - canning mushrooms is very dangerous. The most I would do is pickle them, but even in that case you really need to be careful to get the right recipe.

If you want to make a sauce, plan to freeze it instead of can.

If you plan to store the jars anywhere but the refrigerator or freezer you need to use a thoroughly tested recipe and follow it to the letter. Especially with mushrooms which are a low acid item -- if you don't do it correctly, you run some very serious risks (can you say "botulism"? Not only deadly, but you can't see it or smell it in your product so the only way to be confident it isn't present is either to store in fridge/freezer, or to follow a tested recipe which will likely include pressure canning). Go to http://nchfp.uga.edu/ for tested recipes and more information.