Smallest hi-res HDMI/Thunderbolt display device for Mac Mini

Question

The short version is that I essentially need to have an HDMI or Thunderbolt display attached to my Mac Mini in order to select a higher resolution (1920x1080 or higher), however I don't want a monitor actually attached to it if I could avoid it being that I only use the Mac Mini as a remote device via Screen Sharing.
What is the smallest/cheapest way to accomplish this?

Answer 1

According to the copy&paste from wikipedia, HDMI should support higher resolution than 1920x1200. So the question is, does it aupport that on the mid 2011 mac mini. It says in the specifications
"Mac mini is designed to work with HDMI devices that comply with versions 1.0, 1.1, 1.2, 1.2a, 1.3, 1.3a, and 1.4 of the HDMI specification."
That should mean it should be able to support it, but I don't know : <
HDMI version
1.0
1.1
1.2
1.3
1.4
2.0
Date initially released
December 9, 2002
May 20, 2004
August 8, 2005
June 22, 2006
May 28, 2009
September 12, 2013
Maximum clock rate (MHz)
165
165
165
340
340[109]
600
Maximum TMDS throughput per channel (Gbit/s) including 8b/10b overhead
1.65
1.65
1.65
3.40
3.40
6
Maximum total TMDS throughput (Gbit/s) including 8b/10b overhead
4.95
4.95
4.95
10.2
10.2
18
Maximum throughput (Gbit/s) with 8b/10b overhead removed
3.96
3.96
3.96
8.16
8.16
14.4
Maximum audio throughput (Mbit/s)
36.86
36.86
36.86
36.86
36.86
Maximum color depth (bit/px)
24
24
24
48[a]
48
Maximum resolution over single link at 24-bit/px[b]
1920×1200p60
1920×1200p60
1920×1200p60
2560×1600p75
4096×2160p24
4096×2160p60
Maximum resolution over single link at 30-bit/px[c]
N/A
N/A
N/A
2560×1600p60
4096×2160p24
Maximum resolution over single link at 36-bit/px[d]
N/A
N/A
N/A
1920×1200p75
4096×2160p24
Maximum resolution over single link at 48-bit/px[e]
N/A
N/A
N/A
1920×1200p60
1920×1200p60
Maximum 3D resolution (using a full resolution 3D format) over single link at 24-bit/px
N/A
N/A
N/A
N/A
1920×1200p60