Just in case your flute or piccolo may be misplaced or stolen, you should jot down the make, model and serial number of your instruments. Its very hard to lay claim to something that you can not positively identify.
Here's some guidelines:
1. Call the police and file a report. It may seem pointless at the time, but later you may be grateful that you established an official timeline. Retain your copy of the report. You may need the file number.
2. Canvass the neighborhood. Put up fliers, stick them under doors or on windshields.
3. Offer a credible reward for a "No Questions Asked" safe return of your instrument(s).
4. Check your homeowner's or renter's insurance policy. If you have a policy, you may be covered for your loss. In the future, you may want to list this as a line item on your insurance. By the way, if you are a professional musician at any level and cannot claim status as a student, even if you list the instrument as a line item on your insurance, it probably is not covered. You need to get instrument coverage under a separate policy. Look at http://www.clarionins.com/.
5. Go to every pawn shop in town. Visit them on a weekly basis. This is legwork that you will have to do on your own. The police have plenty of other stuff to do. If you happen to find your instrument, step outside the shop and call the police immediately. Have a copy of your stolen property report.
6. List your instrument as stolen on CraigsList as well as Larry Krantz's flutelist.
If you have some other experience or advice with the loss of your musical instrument, please resp