Occasionally, I`ll see an old violin at a swap meet or garage sale that has been neglected and has unplayable or missing strings. Although it would be a gamble, is there a way to tell if a violin might possibly have good tone if it has no strings? I guess I`m wondering if a garage sale find could be gently thumped like a watermelon or if there are things to look for that might indicate a good tone, other than more obvious things like higher quality wood, lack of cracks/damage and the lable?

Nah...I dun think so. No soundpost means no sound.

When a violin has no strings, you may be able to tell if the violin is decent by tapping with your middle knuckle of your middle finger. Tap towards the center of the top. A deeper sound generally is better. Cheap factory violins will usually have a higher frequency tap tone because they are too thick in the middle of the top plate. A deeper tone usually means it at least wont be a real treble sounding instrument. You can also look down into the f holes and at least see if the instrument has lower corner blocks. Sometimes they put fake ones in but at least if you see no corner blocks it may be a sign that it is a cheap commercial violin...The size of the button on the back is a good indicator as well. A well shaped larger button is better...
for more info,,you can go to my web site.. www.oldfiddles.com I have some info that may be helpful..
Thanks

my trick is to hook up one string... and then give it a good hard pizz. If the sound rings for a long time, it`ll be a great instrument, however, if the sound rings and hen stops abruptly (or seems to get absorbed in to the wood) than i suggest you keep looking. My teacher got her violin this way in an antique shop for a little over 50$ She repaired it, added a chinrest, new strings, etc... and now it`s a great violin... and my teacher is an amazing violinist.. she graduated 1st in her class at a music college in vietnam... that`s unbelievable competition!