Active DisplayPort (either normal or mini 1.1 or 1.2) to HDMI converters can go up to 3840x2160@30hz that's 4K@30hz. They use a Parade PS171 chip to achieve this, however it's not exactly plug and play on the Mac, you have to use SwitchResX. I'm told Windows works just fine on the same Mac hardware. (I'm using a 4K 40' Samsung 40HU6500 TV as a display)
Also make sure the HDMI cable is High-Speed.
Later edit, however your Mac is newer than mine, I have a Macbook Pro Retina 13' late-2012, yours will do these resolutions directly over HDMI 1.3a, but it doesn't have a physical HDMI port, with a High Speed HDMI cable, and it should have DisplayPort 1.2, it could do 4K@60hz easily but there are no converters for that yet, essentially you need to connect it directly via DisplayPort.
Which I think is what you want, IF your monitor has DisplayPort input just buy a miniDisplayPort (Thunderbolt) to DisplayPort Female adapter, this is very cheap and you get any resolution you wish.