I have a private medical insurance policy with INS, it works fine. Already used it, wife had a kidney infection last year and spent four days in CIMA.
You pay all expenses out of pocket and INS reimburses you. So this requires you have a cash or credit cushion, or you'll be S.O.L. CIMA requires a $2k deposit and open voucher on your credit card to check-in.
I got the domestic policy instead of international, but that still covers international care when traveling less than 60 days outside the country (including the United States). I think $5 million max coverage per person, I don't recall.
An annoying thing is INS will only do a SINPE transfer in colones (not dollars), so you need a colon account somewhere if you don't want to get reimbursed in cash. I've a dollar+colon account at Scotia, but 10 times I've complained I can't see my colon balance online and they can't seem to fix it. Although now I've also a corporate colon account with BNCR (by mistake, I setup a Dollar and Euro account, and they did Colones and Euros, so I have all three now).
No one here does checkups at CIMA??