You should be able to work it backwards. If you can determine the coordinate system, size, and "base" coordinate (there is a good explanation of TFW >>here<<) of the ecw file then you could assign that system to your vector data. The provider will have image coordinate reference information.
Align and rubber sheet should be last resorts IMHO - only used if there is no other option. It might be worth your time and effort to get your vector data referenced to the "real world" somehow (control points, survey monuments, etc). It depends on your ultimate goal. If this is a 1 off then rubber sheet it.
TFW ... of the ecw
Well, I would disagree with that, sir.
1] A worldfile does NOT contain any projection data, so you can't figure out to which EPSG a raster belong
2] An .ecw does NOT need a worldfile, because its header contains full projection/location info on the Earth
I think the best resource to work with is a Geotiff, because, once you kept its header, you can edit it in several free tools e.g. Gimp or Irfanview.
And finally, to transform a just-scanned raster into a rich Geotiff, my advice is only one: the opensource Qgis.
I can just do a "move" and most of what I need works fine.
I've tried assigning a coordinate system to my existing drawing, then bringing in my imagery and I must be doing something wrong, because I either get errors or it just doesn't line up.
1) I found a point on Google Maps of my base map to get a lat/long reading.
2) I ran MAPCSASSIGN and set a coordinate system (NE83F specifically) as my coordinate system
3) I converted the Lat/Long numbers into State Plane (NE83F) coordinates
4) I entered a point on my CAD dwg with those coordinates.
5) I moved my dwg using "Move" to using a reference point on the drawing to its "Lat/Long" point I created.
When I try to bring in my new imagery I get the warning "Source Coordinate System not found". What does that mean?
(I can bring in my imagery with no coordinate system defind on my dwg and just move the dwg on top of the imagery, but I am trying to get things geo located in the right spot if at all possible)
What does that mean?
It means that your raster is neither georeferenced nor having a worldfile.
If you wanna line up to a vector map, you must align it according to 2 known coordinates points.
Import that raster thru the _IMAGE command, then run the _ALIGN command to calibrate it.
Finally create its worldfile by means of this tool.
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