lefty_octopus
The best is giclee printing, which is an inkjet process. Typically, the prints last 200 years, and are capable of recreating a large gamut of colors with the smoothest blends. There are specialized fine art printers which have these kinds of printers, but they're expensive, from what I've seen. You can typically ask your local museum if they use such printers for their own work, or know of any in your area. To get past the expense, you probably want to look into Epson's wide format printers, which are also archival and capable of great color reproduction.

Charles Ranker
I've had great results with Vanguard Printing - Any company well versed in large format commercial color printing should be able to handle your reproduction, but like all services it's best to follow a recommendation (even if it's just mine). Another factor to consider, besides quality, is time. Look for businesses large format & publication printing businesses that offer quick turnaround times — same day service is the best, obviously.