It's pretty much strictly linear unless you're talking about very close focusing distances or macro distances. For everything else, what little you may be off is probably less than the rounding error between the actual focal length and the marketed focal length of the lenses in question. For example, a lens with a focal length of 192mm will probably be sold as a 200mm lens. So will a lens with a 197mm or 203mm focal length.

Assuming you are shooting digital, all you have to do is find the ratio of your total sensor width and divide it by the pixel width you have left after cropping, then multiply the result by the focal length of the lens with which you shot the photo. If you crop to a different aspect ratio, use whichever side of the image you reduced by the lower ratio.

Suppose you used a 200mm lens on a camera with a 6000x4000 pixel wide sensor. You then cropped the photo to only 3000x2000 pixels wide. 6000 divided by 3000 is 2.0. Multiply 2.0 times 200mm and you would have needed a 400mm lens to fill the frame with the same field of view you got after cropping the original image.

Suppose you used an 85mm lens with your 24MP camera with the 6000x4000 pixel sensor. You then cropped the image to 1,250x1000 pixels. You reduced the long side by a factor of 4.8. You reduced the short side by a factor of 4.0. 4.0 time 85mm is 340mm, so it would have taken a 340mm lens to fill the short side of the frame with what you had left after you cropped.

In the case of Macro lenses focal lengths aren't directly applicable, since the Minimum Focusing Distance and Reproduction ratio are what matters. Focal length is generally expressed in terms of when the lens is focused at infinity.