I would use something like Baudline. It has a signal generator, and can do a cross FFT. It only runs under Linux, though.
You need 2 cables with 1/8 inch headphone plugs.
One of the cables goes to the line out on your PC, the other goes to line in.
simulate this circuit – Schematic created using CircuitLab
This sets things up so you can do a spectrum analysis of the output of the filter (junction R1 and C1.)
You use the cross FFT, and set Line In Left to be the reference.
The cross FFT then calculates the difference between the spectrums on Line In Left and Line In Right.
Use the noise generator, and averaging to get a smooth plot.
Don't use chirp. I don't think it is synchronized with the sampling, which will cause problems with the windowing.
It will generate a magnitude plot much like the magnitude plote of the Bode diagram on this filter calculator. The difference being that it uses your real filter instead of a simulated one.
You can then change values for R1 and C1 for different low pass filters, or swap R1 and C1 positions to play with high pass filters.
You can do the same with active filters, but then you may need to use a voltage divider to bring the output signal down to something that the PC sound card can use.
You use the cross FFT and two inputs to automaticall account for the frequency response of the soundcard outputs and inputs. Different loading of the output can cause the frequency response to change or to be distorted. The two connection method I've outlined accounts for that automatically.
The one catch to this method is that you may have to swap left and right. They aren't always the way you expect them to be. If you hook it all up, and the response is upside down, then swap the input channels. You can do it in the software or by changing the physical channels.
If you need detailed instructions, let me know and I'll write them up. I don't have Baudline at hand right now.
Baudline also includes a function generator, so you could send various types of signals at differing frequencies through your filter and observe the effects on your oscilloscope.
I'm sure there are Windows programs that can do the same. I use Linux, though, and Baudline is an old friend.
If you go looking for a comparable Windows program, look for one that includes a signal generator and that can do cross FFTs.