You can travel to Kosrae on United Airline’s Island Hopper route via Hawaii and Guam four times a week. If you want to visit Kosrae and some other islands in the FSM, you can contact United desk for the “Visit Micronesia” ticket.
Coming from Europe, around-the-world tickets can be purchased at a reasonable price to include Kosrae and other stops with a maximum travel time of 1 year. Visit Staralliance or ask your travel agent for details. Apply for a onepass number, and with the miles you’ll earn after travelling to Micronesia, you can save almost $1000 in another travel or to come back!