Upres Image

Photoshop can upsize but as you experienced, the results are pixellated and fuzzy. As c_pfaffenbichler suggested, you may be able to improve on your results. But, depending on your quality needs and how much the image needs to be upsampled, it is quite likely that the image may still not be acceptable. 

Illustrator cannot resample like Photoshop can, therefore the pixels in the image will simply get larger when you enlarge it in Illustrator, resulting in pixelization. Illustrator has an image trace feature that would allow you to convert the image to vector, but for low resolution images the results are usually quite poor.

You could post the image for further advice, but my guess is that you are wasting your time and would be better off with a higher resolution image.

Please post the image and state how large you need it to be exactly. 

Photoshop (and naturally most other image editors) can upsample images, but the result depends, apart from the amount and the quality of the source image, on the Resample Method. 

Which ones have you tried? Did you try the »Preserve Detail«-ones? 

Have you tried an image search or a reverse image search to determine if the image may not actually be available larger anyway?