How to capture 4K screens?
As you know there are two solutions, one using your CPU, the other a dedicated GPU.

CPU Solution

As of today, the CPU solution exit for 4K content, at 60 fps, using x265 or x264 codec. x264 is embededded in OBS in fact, and x264/x265 are known for being the fastest implementation of the standard H264/H265. But, you need a powerful CPU, of course, and then you'll have to make trade off regarding the file size and/or quality. FYI, the x265 has been demonstrated to be able to live encode H265 stream 4K 60 fps, but using a dual socket server (not a standard CPU). It was last year.

GPU Solution

nVidia released end of year 2015 the fist cards with 2nd generation Maxwell architecture that is the first allowing H264 4K live encoding.

Since the Ultra High Definition streams needs a lot of resources, you couldn't really find an acceptable solution before new CPU or GPU are released. If I were you I would go with the GPU solution because you could use that card for both display and capture on the fly. If you could afford it of course, such nVidia card are pretty expensive!