Since COBRA insurance is a continuation of your previous health insurance plan, under the COBRA insurance laws you will be able to continue to see the same doctors and specialists as you previously had at the same expense.  This means that any doctor that you were previously covered to see with your health insurance plan will still be covered.

But what if it is a new specialist?  That is fine as long as the new specialist would be covered under the medical insurance you have at your prior employer.  The plan continues exactly as it had before so the costs incurred are the same.  If you would have been charged under your previous plan, you will be charged under COBRA health insurance.  If you would have been covered, you still will.  Check to make sure the specialist is within your care network with your insurance provider and inquire with the insurance company to determine costs for anyone outside of the network.  The cost will be in line with your previous health insurance plan and their charges for outside of the network coverage.