I'm running an experiment and I need to have a container filled with water. The container will be placed inside a microwave oven, but I need to minimize any effect the microwaves will have on the water. How can I go about running my experiment? I'm thinking I need to insulate the container with some kind of material that will shield the water inside from the microwaves generated by the microwave oven.
Unfortunately, you are in a bit of a bind. You need a combination of things to successfully achieve your experiment, and I doubt you be able to achieve it using a commercial microwave oven.
First, you need to build a faraday cage around the section you want to not be exposed to microwaves. Faraday cages (https://en.wikipedia.org/wiki/Faraday_cage) provide a means to prevent RF energy from penetrating a fixed area by protecting that area with a conductive ground plane (to shunt the RF energy to common ground). In fact, the microwave itself is a faraday cage, simply built to not allow the radiation to escape. Unfortunately, commercial microwaves are not designed to allow you to put a faraday cage inside (they will arc), and I would be very cautious about trying to run a grounding line through the door (as this would prevent the oven itself from being an effective faraday cage).
In order for the faraday cage to work in your experiment (I will assume that your vessel has a cubic shape, just for the sake of discussion), one wall of the faraday cage also needs to be a semi-permeable membrane. This will allow whatever mass transfer you are trying to evaluate, but still prevent radiation from entering the fluid inside the faraday cage. While it is possible to make a faraday cage from a frequency selective surface such as the door of the microwave (https://en.wikipedia.org/wiki/Frequency_selective_surface), it would require a custom design and fabrication to make it out of your semi-permeable membrane. In addition, the metallic mesh used in the FSS would certainly have an impact on diffusion through the membrane, and that might not be acceptable to your study.
Starting from scratch, what you really want is a source of microwaves, a waveguide and a test area within the waveguide which will expose some of your materials to the RF energy, and keep some of it shielded. This is doable with waveguides, which use good design to shape the flow of the RF energy, and would result in minimal exposure (but not zero) of your material. There are many good references here (http://www.microwaves101.com/encyclopedias/waveguide-primer) but for your specific instance you need someone with detailed knowledge about waveguide design, and the ability to tailor it for your experiment.
A more fundamental question is whether you need to provide microwaves for your experiment because they are a source of heat, or because they are a source of RF radiation. If you are simply using them for heating, I would suggest an alternative like heating elements/blankets or a specific heat source (burner, steam mantle). If you are using the microwave for its RF energy, then you may be forced to pursue the complicated waveguide solution.
I hope this helps, if you can post more detail I will provide edits.