Is there any pain involved in an intrauterine insemination?

No. No. It is a simple procedure. It should not cause pain. Sometimes the actual procedure only takes 2-3 seconds and usually it takes less than 20 seconds. Some women feel cramping for a few seconds but that is usually it.
Minor. The amount of pain with an intrauterine insemination (iui) as performed by an experienced reproductive specialist is minimal or none. Unless you have scar tissue in the cervical canal due to a severe infection or an infection post abortion the pain is minimal, certain no more than inserting an iud.