A jeweller will re-size a ring for you, and it shouldn't cost you much.They will remove a section of the ring, in this case a couple of millimetres, and re-solder the ring back together.They will use platinum solder so that your ring can be legally stamped, or retain it's stamp.DIY is not a good idea if you don't have any experience with precious metals.
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If you don't want a jeweler to do it, there is a product called Ring Guard Solution. It's a clear gel that will last a couple of Months. Google Ring Guard Solution Also an item called Ring Snuggies.Here is a YouTube Video of Ring Guard Solution
Have it done by a jeweler! - Make sure you keep or get a cost reduction for the material they remove and (often) keep.
I would recommend visiting a professional jeweller, due to the sentimental / emotional value of the ring.
I know jewelers cut a segment out of a gold ring and remelt the ends back together followed by shaping and polishing.A
You can temporarily line the inside of the ring with layers of adhesive tape until it fits better, or get a jeweler to put a 'ring reduction bar' inside it, which isn't very expensive. However getting it actually resized smaller is a bigger job, and depending on the value of the ring, it might be best to have this done with a jeweler rather than a DIY method.