Scaled up low resolution 2D game

Hello!

I am creating a 2D game with NES style graphics. I use simple textures without mipmapping and point filter. For moving objects (sprites I wrote a shader which snaps their vertices to integer values or fraction of integers, in my case it's 1/8th unit since my sprites are 8 pixels per unit sized. Camera is snapped to 1/8 unit too.

But I am thinking about to use another method. Maybe it'll be little bit slower, but I want to render the game its "native resolution" (256x224) and upscale it to 2 to 4 times bigger. But I have no idea, how should I do this. How should I render my screen in low resolution and upscale it to a higher without any distortions?

I tried to render to texture, but the result was distorted. Also if I increase the resolution, the whole thing will be bigger, it'll render the texture from the bigger screen into... like a 256x256 texture and I think it may cause distortions again.

What is the best way to render and scale up the graphics pixel perfectly?