The refurbished iPhones listed on RefurbMe don't come with a SIM card—unless stated otherwise on the merchant's website.

In general, refurbished phones are sold independently from phone plans and contracts. Professional refurbishers tend to work on devices only (i.e. they're not carriers). That being said, you could find a refurbished iPhone that comes with a SIM card, so be sure to read thoroughly the information provided by the merchant.

If you already have a SIM card and a phone plan, make sure you buy a phone that is either compatible with your carrier or unlocked (meaning that it will work with any provider).