Do you really mean "without losing pixelation"? Normally we all try to avoid increasing pixelation. Pixelation is when the individual pixels in an image become visible to a greater or lesser extent. If you mean you don't want to increase pixelation then it depends on the size and resolution of the website photo and how much bigger you want it to be.
As David is suggesting, you are probably going to be unlucky. Especially if it really is a small web graphic. If you start with an image 500 pixels square, than it is going to look terrible if you merely double the size to 1000 pixels square, which is not particularly large anyway.