Try Fabric Tack, available at most hobby stores and WM. It can be removed if you ever decide to change the set or take apart. Also easy to roll off excess if needed. Will attach to 99% of anything and lasts. I've used it on broken china, metal, fabric, even to patch carpet. Love this stuff.

What about a heavy duty double stick tape?

emagineer, you got me thinking about hot glue. I wonder if that would work too? I don't want to ruin the silver, so am not sure how easily it would come off.
dawnp, I could try that too, but I don't know if that will stick any better than the velcro?
Any framer's out there that can tell me how its done? I'm thinking a small gage wire around the 'neck' of the spoon or fork and twisted in back to hold in place? How do I make such a small hole to thread the wire through the backing?

I have my MIL's baby spoon (she gave it to my DD) in a shadow box. I've had the best luck with a bubble of sticky tape. That's after trying a bit of 3M peel off stuff, glue dots (scrapbooking stores carry them), and that semi stretchy glue that comes on mail flyers.

So of course, the only pic I have showing it also makes it look the spoon is crooked & has fallen down. It is neither, I promise. :)

For the wire idea (which is what I've seen at my framer's and which I used once): Is there a removable backing board in the frame? Take it out, place it flat on a surface and place the spoons down on it to determine your placement. You might find it easier to mount them perfectly vertically, instead of angled (I know that'd probably look boring, but you'll get an easier mounting and they are less likely to slip over time).

Then of course somehow mark the mounting board to figure out the placement of the holes for the wire. Use a very finepoint marker (I'd try to find a silver one so you don't get any tell-tale marks when the project's all done).

Here's how I got the holes in the backing board for the wire: I placed the backing board over a piece of wood, then gently hammered a skinny nail where I'd made the marks.

(I used this technique to do a display of fountain pens in a black shadow box. Sorry, no pictures -- after a couple years I took them out because I found an acrylic stand for them that I thought was much cooler for my space.)

One other thing: As an alternative to the fine-gauge silver, or silvertone wire, which might turn color over time, you could experiment with using clear fishing line or the clear beading line that's sold with the jewelry making supplies in ACMoore and Michaels and such.

Beading stores sell sterling wire that might age similarly to the spoons.

Kmcg, please let us know what you end up doing. I have 5 or 6 baby spoons/forks that were mine and my siblings. My mom hung them on a spoon rack, but I'd love to find another way to display them.

I have several shadow boxes with various things in them. Baby dresses were sewed, as was a vintage evening bag. A have one frame with skeleton keys from my family's furniture store they owned for over 70 years. Most of those are held on with hot glue. A couple they used wire. It also depends on what you are using for the backing (of the shadow box). The dresses are velvet material and the evening bag is a textured silk/linen matt board. For the keys I used handmade paper.