I found a guide to extracting N64 models from 2004.  It's a little confusing, outdated, and uses 3DS Max in the latter steps; but I figured out most of the process.  You should be able to put it together between the original guide and my notes.  For sake of expediency and in case the original page goes down, I'll paste the relevant passages here.

---Step 1. Preparation---

a. First, make sure that you have the necessary tools to complete this process. If you do not have everything, stop and obtain them all first.

He recommended Nemu64.  The emulator I used was 1964.  I had to download Darkman's Input Plugin to get it to recognize my Xbox 360 Controller.  The video plugin he mentions is here--you put it into the plugins directory.  If you get a message saying glide3x.dll is missing, you can find that here--drag it into the main 1964 directory.

b. Create a folder in your hardrive folder - C:\ - titled VRML. This file path is set in the emulator as the place to export the VRML file and the associated texture BMP's.

c. Extract Nemu 64 from the zip onto your desktop. Leave it there. You might be able to change it't location, but I found that doing this messes up the emulator - I don't know why.

I just extracted 1964 to my games directory.  You can put it wherever you want.

d. Create a folder somewhere, anywhere, where you will keep your roms. This in not necessary, but it will help you stay organized.

e. Open Nemu 64 and go to the "input plugin" window by clicking the controller icon or clicking "input plungin" under the "plugins" pull down menu. If you have a gamepad that you would like to use, click select input devices and select your gamepad. Make sure that controller 1 is "plugged in" and assign the n64 buttons to your gamepad or keyboard.

This is confusing because he's talking about Nemu64.

Plug-ins > Change Plug-ins > change the video plugin to Nemu64 Graphics (combine debug)

If you installed the Darkman's Input Plugin, it's setup by default for keyboard controls.  You can always map a controller later.

 ---Step 2. Extraction---

a. Open the rom file that contains the desired model and wait for the game to load. The emulator will display the progress of the loading and then start the game.

b. Get to the area/level of the game where the desired model can be clearly seen. Press F4 to pause the emulator.

Press F3 to pause the emulator.

Plug-ins > Video Settings

c. Open the "video plugin" window and check the "export VRML" option. Click OK. Rapidly press F4 (F3) twice to quickly unpause and repause the emulator. The reason for this is that you only want to export 1 frame of animation. More than one frame will cause missing faces in the geometry.

Letting the video play too long causes all kinds of glitches.  Even if you do it just right, it may not capture every model on the screen or may show other glitches--I'm not sure if that's a compatibility issue with the game or maybe the viewers I was trying before I found one that seems to work.

--- Note that large game areas have problems opening in 3d Studio Max. Try to stay in a small room when exporting the VRML. If the desired model is a weapon, try to extract it when it is not in the hands of a character. This can complicate the cleaning of the VRML. Extract the weapon while it's on a floor or while in the start menu (i.e. Goldeneye). If the desired model is a character, pause the emulator while the character is standing in a basic pose. --

I haven't confirmed that about the large areas yet.  It's possible.  The meshes seem to all weld together, so you would want meshes as separate from each other as possible when you capture.

d. Open the folder C:\VRML and see that there are now many BMP files and a VRML file. The BMP files have numbered names. Don't change these. The VRML file is titled "output.wrl" If there are no contents in the VRML folder, retry the previous steps.

---Step 3. Editing the VRML---

I stopped reading here.  If you have 3DS Max and Milkshake, follow the link back to his guide.

The emulator is hit and miss on compatibility.  I got a couple of games to work by changing video settings or changing the video plugin (there are several you can download), but the only one that will export the models is that LemD3D8.dll; so, if it won't display the game properly, you probably won't be able to rip the mesh you want.

I tried several free and shareware VRML viewers before settling on Flux Player and Flux Viewer.

This is from the opening sequence of Super Smash Brothers.  You may notice a couple of graphical glitches, but I think it most cases one would use this to extract a single model from a scene, so that shouldn't be an issue.

Flux Studio can export into several common formats, but I couldn't get any of them to import in Blender.  I think there might be a problem with my Blender and/or Python install.

I exported as Wavefront .obj and imported that in DAZ Studio.

There were similar minor problems, but I thought it looked pretty good there.  Depending on the game, you could add some lights, adjust the material settings, and get some decent renders.

After exporting from DAZ, experimenting a couple of times with the checkboxes for the importing options, I was finally able to import into Blender.  Only problem:  No textures!  And I can't see a thing when I try to zoom through the outside wall into the room.  If I changed it to edit mode, though, so it's in wireframe, the shapes are all clearly there.  So this should at least work for ripping meshes.  I can figure the rest out later.

Now, Flux Viewer says it's a full-fledged image editor, so it may not even be necessary to go into DAZ Studio or Blender.

Once you've separated the model you want from all the other meshes in the same, you just save it and move on to Civfreak's guide for getting it into Havok format and into the game.

It's also worth noting:  There are tons of free VRML models online, so knowing how to convert those for use in Elemental could help, even if you don't want to steal props and things from N64 games.