OK, perhaps you should study your workflow.
If you Crop a Clip in a Sequence, then output that as a discrete file, to be Imported, the areas of the Crop will be black.
Instead, I would suggest placing that Clip (the one to be Cropped, to create a PiP - Picture in Picture) on a higher Video Track, and then Cropping it there.
If you must Export that Cropped Clip, Import that output file, and use it in your new Sequence, you can just apply the Effect>Crop again, to remove its black, or use the 4-Pt Garbage Matte, to remove it.
Adding to Bill's advice, if you encode a clip or sequence that you want to round-trip to use in Premiere, go for a lossless or near-lossless codec. WMV is not a good choice because you're introducing a "lossy" compression cycle, which will necessarily degrade the quality of your eventual finished video. If you let us know which version of Premiere Pro you're running as well as the platform you're on (Windows or Mac), and also the resolution of your video (height and width), we'll recommend some good export formats to use.
That said, Bill's recommended workflow is right on the money. For what you're asking about, you do not need to export the clip that will be the PIP.
I agree completely. When I need digital, intermediate files, I rely on either Lagarith Lossless, or UT.
For many reasons, I steer clear of WMV, unless that is exactly what the client needs for deliver-only, streaming media.
Good point, and one that I should have covered.
I understand your directions and I have successfully tried them. On the cropped and imported clip I was trying to Edge Feather all edges - including the cropped top and bottom. Importing the cropped file and recropping didn't provide this function. Do you know how I can achieve this effect, e.g. Edge Feather on cropped edges? I tried Glow but that's isn't quite the effect I am after!
I am on a PC, Windows 7, using Premiere Pro CS6. This video is 1440x 1080
To get full control of the Crop, instead of Edge Feather, I would suggest that you look into Track Matte Keying. You can create a Track Matte, then either use a Blur in PrPro, or create it with such, in Photoshop. Edge Feather sounds like it will do what you want, but it is really a different Effect.
Good luck, and if you need some help with Track Matte Keying, just let us know, please.
In my experience, edge feather and similar effects that funciton on the edge of a source do not honor cropping. That is, the effect is applied at the original edge of the source, not at the cropped edge. If there's a way to get around this, I haven't discovered it.