Remake maps is usually a hard thing to do. You have to make it not only look like, but also feel like the original one. And base on that, you can then add your own flavor into it.
But it's very difficult, even just to make it look like. Every game has its own style and gameplay. The scale of map is also different. Unless you are very very familiar with the original map, you can't really make a copycat without any handy tool.
So here, I'd like to show you a simple solution of "HOW TO Export A QUAKEIII MAP FOR UT3", or precisely, how to do that for remaking in UED4.
1) First off, you need to get GTKRadiant. It's a famous game editor (kinda like UED) for games based on idsoft's engines.
2) Just download the GTKRadiant installer and install it wherever you like.
3) Make sure you have Quake3 installed.
4) Install 3dsmax or maya, or any other 3d modelling software that can import obj(wavefront obj) file. I use 3dsmax here.
5) The geometry of a Quake3 level is compiled to a bsp file for the engine to run it ingame. But GTKRadiant doesn't open bsp file directly. So we need to decompile it to a .map file so that the editor can open it and export the brushes.
6) Go to "Your Quake3 directory\baseq3", look into the pk3 files (they can be opened with winzip or winrar), and you shall see "maps" folder, click into and see bsp files. You have to check pk3 files one by one to look for the one you want to remake. When you find it, extract it. I suggest you extract it to "Your Quake3 directory\baseq3\maps", as this is the default map folder for Quake mapping.
* Go to "baseq3", and open pk3 files with winrar
*Click into the "maps" directory
*Extract the one you want to convert
7) Go to "Start-->Run...", type in "cmd" in the pop up window, and run Command Prompt.
8) Type in "cd Your GTKRadiant directly". (e.g. cd "C:\Program Files\GTKRadiantā).
9) Type in "q3map2.exe" -convert -format map -fs_basepath "Your Quake3 directory" -game q3 "Your Quake3 directory\baseq3\maps\YourMap.bsp"
10) Something like: "q3map2.exe" -convert -format map -fs_basepath "E:\Quake III Arena" -game q3 "E:\Quake III Arena\baseq3\maps\pro-q3tourney4.bsp"
11) The bsp file is decompiled and a map file is create in the same folder.
12) Run GTKRadiant, select Quake3 as the preference. Open the map file with "File-->Open" menu.
13) You shall see the level now. And press Escape to make sure you don't select anything, and then press "I" to inversely select everything. (You can also do this with the menu)
14) When the brushes are all selected (don't worry about the entities being selected), go to "Plugins-->brushexport2-->Export selected as Wavefront Object".
15) A window pops up, choose "Don't collapse" if you like to export them as individual brushes, but here I choose "Collapse mesh" since I gotta use it in 3dsmax as a reference. Click "Save" and you get an obj file.
16) Run 3dsmax (or other modelling tools), import that obj file, make sure you don't select "Rotate model" when the below window pops out:
17) Now you can see the whole bsp of that map in 3dsmax, but before going further, we need to make sure the scale is OK for UT3.
18) Make sure you reset the pivot of that bsp level to the origin of the world.
19) I did a couple of test, and found the bsp level from a Quake3 map has to be upscaled to 175% to suit UT3 (of course you can try from 150% to 200%, but the best turns out to be about 175% or a little less).
20) Sometimes the polygons of the bsp level are upside-down, you have to filp them.
21) Now you can simply export the bsp level as an ase file which can be imported into UED4.
22) Or you can use it as a reference mesh for further custom modelling.