None of those are licenses. The only license involved is the ordinary real estate salesperson or broker license issued by the state you practice in, and the requirements for that differ by state. Nothing in any state's licensing scheme distinguishes a $10M house from a $300k house.
CLHMS, from the Institute for Luxury Home Marketing, is a designation. You take training, meet a sales performance threshold, pay for it, and keep paying annual dues to display it. Course fees in this category commonly run in the several hundred to low four figures range, with dues on top. Luxury Property Specialist and the brokerage-branded programs work the same way. They're marketing credentials and training, and they carry no legal authority.
On insurance, errors and omissions coverage is usually carried by the brokerage with agents named under the policy, and agents typically pay a per-transaction or annual contribution toward it. The policy has a per-claim limit and a deductible. At high price points the limit is the thing to actually read, because a claim tied to a disclosure dispute on an expensive home can outrun a modest per-claim limit, and the deductible is often the agent's responsibility. Some agents carry their own supplemental policy. What coverage is available and what it excludes varies, so get the actual policy document rather than the summary sheet.
The exposure that tends to get underweighted isn't the designation question at all, it's wire fraud. Escrow deposits on luxury purchases are large and attractive, and the losses land on whoever's email got compromised. Whether E and O responds to that at all depends on the specific policy wording, which is worth confirming in writing with the carrier.
