how can I insure a shipment for more than $10,000

A few additional things you should do if you ship high dollar value items (above the  maximum insurance levels) with FedEx or UPS.  The company I worked for prior to my retirement used to ship high value metals all the time and FedEx/UPS provided guidelines for us.  (Some shipments were approaching $1M USD. )

• Use descrete packages,  i.e. blank boxes.  Don't do anything to advertise what the contents are.
• As @gregrolka mentioned, you need to seal every edge, corner, etc.  And use "tamper proof" printed tape.  It makes it a bit more difficult to slit the box open and then retape it.  You can get it on Amazon.
• If handing the package directly to the driver, make sure he/she is aware of the value.  Their protocols should have them segregate the package in the truck so it can be locked up when it is unloaded at the depot.
• Otherwise, take the package to the actual FedEx or UPS desk at their respective shipping centers, not at the UPS Store or Walgreens, etc.  One, you will get a better rate, and more importantly, if you let them know the high value, the supervisor will lock them in the "cage" until ready to be placed on the truck/plane.
• Ship overnight or 2 day delivery instead of ground if possible.  Fewer transfer points and hands on the package.  Less likely to get misplaced or "lost" in transit.

I have found using the Mail to insure, has been $$$$.  If you can put the equipment on a palette, most trucking companies have very low insurance costs.  I suppose the reason is they rarely have to pay a claim?  A pair of amps I shipped recently, insured for $40,000, cost me $65 for the insurance.  Cheers.

Registered mail through the US post office is your best bet.  You can insure any shipment for up to $50,000.

It’s cheaper than buying insurance from FedEx or UPS.  And it’s very safe—your box will be locked up during the shipment process.

However it can be very slow.  It could take anywhere from 7 to 18 days to be delivered from my experience.

You also have to seal every edge with brown shipping tape.  You can find the tape on Amazon.  It’s the type you have to wet down with water to stick.

I’ve shipped almost 100 packages using registered mail and every one was delivered.

I took it to Fedex. I don't know what the limit is , but they did go $19K. It looks like the 3rd party sites that offer discounted shipping have their own limits. The ones I am used to using cap it at $10K. 

all good... thanks

what is a dealer? That is only half joking.There are no high end dealers with 3-4 hours of me. Even if there were, I can't afford to buy what I want working with a dealer, so like most of us, wheel and deal on sites like this. 

and I'm talking about selling a used item I have, No dealer is going to help me do that.

I am not sure of your situation. But I have my dealer do everything, so I am never in a position of shipping anything like that. 

Guess I'd be focused on finding which either insurer or shipper actually stands behind the insurance if a claim needs to be filed; how the items needs to be packed and by whom with proof of such; what needs to be in place as proof of item and packaging condition prior to shipping, and what's required afterwards. Nothing is ever straightforward in these matters

They mail diamonds all the time at the USPS. 

I think, USPS Registered Mail could be insured for up to $25k, unless they changed it. But I have no idea about either the cost or weight limits or etc. Registered Mail is also very slow, but very reliable.

looks like DHL and FedEX will go higher if you book direct rather than through a 3rd party like PayPal ship or Pirate Ship and others.

If you have your policies with high net worth type insurers, e.g. Chubb, Pure, they can write riders that will cover your while gear is in transit. I did this when I moved from NY to Texas because the mover’s insurance is based on gross weight of load and is largely worthless. I wound up keeping most of the riders in place, but there is no reason I can think of why you can’t discontinue the coverage. Usually, such companies want all your business- home, autos, valuables + umbrella coverage. I found this years ago when I bought my first exotic car- the normal insurance companies wanted a fortune to cover the vehicle. I got to Chubb and it was a fraction of that and I shifted all my coverage to them. Unfortunately, Chubb’s rates are quite high, I think in part due to the wildfires in California. We now use Pure, which is a similar type of insurance. But this means changing insurers. I doubt they will write a policy as a one-off if you aren’t a client. 

PS: I'm not in the insurance business and somebody who is can probably answer your question more fully including whether any companies will write limited term insurance without being a regular client. 

Good luck,