Despite the rumours flying around of Sega announcing Shenmue 1 & 2 HD re-releases on XBL / PSN we still have no confirmed evidence that this is going to happen anytime soon, as Sega seem to be totally disinterested in the Shenmue franchise. Therefore if you want to grab yourself a piece of Shenmue HD action (or as close as your gonna get to it) then i would highly reccomend converting your Dreamcast setup to get the best out of what your console and TV has to offer. Amazingly for its time the Dreamcast console featured VGA output, to achieve a 480p signal, whilst no other sixth gen consoles have this feature. To take advantage of this you will need the following items:

Dreamcast console (obvious)
High Definition TV with resolution up to 720p or 1080p
Dreamcast VGA box or cable (box is reccomended)
VGA - HDMI Upscaler / Converter box
Standard HDMI lead
3.5mm headphone jack audio cable
Set of PC speakers

This is the equipment i am using in my setup, and below the beautiful screens of the game running on my HDTV i will explain further how to set everything up!
Click on the images to enlarge
First of all you need to run the VGA box from the back of your Dreamcast A/V out port and plug its VGA cable into your VGA>HDMI converter box, which will also need to be plugged into a power source of its own. You will also need to run a set of PC speakers from the Dreamcast VGA box to get sound out of your Dreamcast, the connection is a standard 3.5mm headphone socket. Then you need to run a HDMI cable from the converter box to your HDTV. Finally turn on your Dreamcast & TV, put it on the correct HDMI channel and hopefully you should see (and hear) the Dreamcast boot up screen. Most converter boxes will allow you to choose between 720p or 1080p with a button on the box, have a play around with this and your TV settings to find the best picture for you, i found it looked best on 720p and on my TV's GAME setting. Not only does Shenmue look amazing but other Dreamcast games are also breathtaking, check out some screens below of a couple of my favourite Dreamcast racers.
Tokyo Highway Challenge 2 (Click to Enlarge)
Le Mans 24 Hours (Click to Enlarge)