I'd really like to use LibGDX for this jam, but I'm not quite sure how to emulate the 64x64 resolution in this engine. Does anyone have any idea how to do this?

Glad to see people using LibGDX :D
It's quite simple actually, you need to take advantage of the Viewports, more specifically FitViewport.
Documentation: https://github.com/libgdx/libgdx/wiki/Viewports

Let me show you some snippet for a Screen class which will always maintain the 64x64 aspect:

public class LowResTest implements Screen {
 private Color color = Color.BLACK;
 private Viewport gameView;
 private SpriteBatch batch;
 private Texture texture;

 @Override
 public void show() {
  gameView = new FitViewport(64, 64); // This is the internal resolution your game will display regardless of window size
  batch = new SpriteBatch();
  texture = new Texture(Gdx.files.internal("badlogic.jpg"));
 }

 @Override
 public void render(float delta) {
  Gdx.gl.glClearColor(color.r, color.g, color.b, 1);
  Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT);

  gameView.apply(); // we set this as the current viewport (we could have more viewports, for example a hudView)
  OrthographicCamera cam = (OrthographicCamera) gameView.getCamera();
  batch.setProjectionMatrix(cam.combined); // Don't forget this else your viewport won't be used when rendering
  batch.begin();
  batch.draw(texture, 0, 0);
  batch.end();
 }

 @Override
 public void resize(int width, int height) {
  gameView.update(width, height); // also don't forget this
 }

...

Hope this helps!

And good jamming to all! I still have to spend some day to brainstorm ideas :P

Thanks for that robonutria I'll be using libgdx as well myself.

Hey thanks! I am going to be trying this in libGDX too