In Photoshop,
Image->Image Size->Check "Resample Image", select "Nearest Neighbor (preserve hard edges)"
Then just set the new size at the top of the box in either the Pixel Dimensions or the Document Size.
This will get you what you want, and quick!
I find for sprite art prints, putting an outline around the blown-up sprite using the
Outer Glow Layer Style helps. You can use
Outer Glow to create outlines with a few parameters.

Clear the background, so you have the sprite by itself in the layer.
Right Click on your sprite layer and click
Blending Options, this'll open the Layer Style window.
Click on
Outer Glow, set the
Blend Mode to Normal and the
Opacity to 100%. Set the colour to Black (or whatever colour)...then
Spread to 100%. You can then play with the
Size to get the outline thickness you want.
This is a decent quick effect to get rounded outlines that will retain detail when you scale the image, makes sprite work easier on the eyes when at a larger scale
