Since I don't know what you're trying to paste into I'll hit several areas relating to this.
Copy image places more than one format on the clipboard. If you're pasting into Word, then a 'Paste' operation will place a Bitmap format in the document. Bitmaps will be fuzzy unless they are sized at exactly 100%, which is probably what is giving you the 'low resolution' feel. However, if you choose 'Paste Special' and choose 'Picture (Enhanced Metafile)' as your format, then you'll get a vector graphic which draws much better.
The one disadvantage here is a gdiplus bug (low level system API well below NORMA, VS, or .NET) that leaves an uninitialized field in the generated metafile stream. This causes issues with some programs (not Word) and print drivers. If you see big purple blobs, then you know you've hit this problem.
The alternative is to use the web viewers, which display all of the ORM diagrams, but not the relational ones (at this point). Run http://www.ormsolutions.com/tools/orm.aspx or http://www.ormsolutions.com/tools/ormPrint.aspx from Chrome or FireFox to load .orm files from the local system into your web browser. The first page does one diagram at a time with a dropdown to select the alternate pages; the second loads all diagrams on a single web page. From here, you can either print to pdf (Adobe tools come with this feature, there are also free pdf printers like Bullzip that let you do it), or you can dive into the page and grab the generated svg as follows (for the orm.aspx page):
Using Chrome, load the model and diagram you want the svg for.
Click the Elements tab on the console toolbar to see the current html
Expand the body element, the diagramPaper div, and the diagramPaper_svggroup div
You'll an svg element. Click on it to select it.
Right-click and choose 'Copy as HTML'
You now have the svg representation of the diagram on the clipboard and should be able to use this with any tool that accepts svg
Unfortunately, integrating svg into Word is not directly supported. A quick web scan shows some free and not-so-free utilities to do this, but I haven't looked into them. Has anyone else researched this area?
Both the metafile and svg versions are vector graphics and render cleanly at any zoom level. Maybe you can let use know the program that you're trying to paste the graphics into?