Nana, the resident health insurance ninja in our household, arranged for us to get some annual checkups down at Yonsei Severance Hospital's International Clinic yesterday.
Though we've said so on this blog before, it bears repeating: service in the International Clinic at Severance is absolutely superb. They have several English-speaking general practitioners on staff, plus several English-speaking guides and nurses who escort you wherever you need to go outside the clinic (for example, for blood work or x-rays, etc). They also have walk-in hours on Saturday mornings, though be advised that many of the hospital's specialists only see patients during the week.
Apparently, Gangnam Severance has also opened an international clinic, though we can't report on their service first-hand.