A longwire aerial has an impedance of 600-650 ohms. Your shortwave radio may have an input impedance of 50 ohms or could be much higher. Most small portables have probably fairly high input impedance and won't match very well when connected directly to a longwire aerial. There is no real problem with this except that you are not extracting the best signal level from the aerial. If you were using a transmitter a mismatch would result in large voltages which could damage your radio output stages and cause overheating or breakdown in the output path. There are a few things you can do which will solve a couple of issues when connecting an aerial to a SW radio receiver.

1) Use an aerial tuner to present a 50 ohm environment to the aerial. Then connect the tuner to the SW radio. The advantage is that you will reduce interference from strong stations that modulate down and cause weak stations in the tuned band to be swamped. The second advantage is that you can match the tuner to the aerial with a fixed transformer.
2) Use a transformer to impedance match the aerial to the 50 ohm load (be it the tuner or your radio itself)

I use an MFJ-956 SW/MW/LW tuner to connect to my longwire aerial to my receiver. In addition I built a small transformer which connects between the aerial and the tuner. Here's a schematic of the setup.

Here, the source is actually the aerial tuner. The setup above actually shows a way of measuring the impedance transformation ratio. I was hoping for a VSWR (voltage standing wave ratio) of 1 for this setup with a 50 ohm load for the aerial, however, I got a somewhat higher result. In fact, the best match occurred with a 75 ohm load. A high VSWR implies a higher level of mismatch. In fact, in a transmitting aerial the voltage levels on the feed line and aerial could be VSWR times the actual designed values (based on perfect match). This is what results in insulation breakdown or damage to output stages, not to mention the heating and other losses.

From my calculations, if you assume a 600 ohm aerial impedance and connect to a 50 ohm load, the VSWR is 12. The reflection loss is 5.5dB and return loss is a poor 1.45dB. If perfectly matched, the VSWR would be 1, the reflection loss would be 0dB and return loss infinite (strange, but true!). The turns ratio is sqrt(Z_load/Z_src). In this case, this was approx 3.5. I used a 3/4" diameter toroid and wound it in a bifiliar manner using magnet wire. The actual number of turns were 10 on the primary and 35 on the secondary. You can adjust the actual number of turns higher or lower as desired.

The following graph shows the VSWR versus frequency for two calculated impedances, 50ohm and 75ohm. An unmatched connection from a 50ohm radio input to a longwire would have been nearer to 12.

I used an ICOM IC-R8500 receiver to do the measurements on the before an after performance with and without the toroidal transformer.

Here are results from the S-meter for several data points
 

Freq, Hz	Before imp match, dBm	After imp match, dBm	dB improvement
6.80E+05	-53	-48	5
1.00E+07	-82	-76	6
1.50E+07	-76	-70	6
2.00E+07	-88	-83	5

A 6dB improvement corresponds to 1 S level in signal strength