I am not well versed with transmission line theory so if you can redirect me to relevant material I'd be grateful. So I used Agilent 4294A to find resistance of a 2 metre long shielded twisted pair cable (BELDEN 3105A E34972 1PR22 SHIELDED) and the resistance across frequency looked something like
with a discontinuity at 5MHz. At 4.99 MHz it was about 2.04 Ohms and 23.5 Ohms at 5.01 MHz. This trend was there in impedance as well. I feel I'm missing something fundamental here.
Your tooling seems to be the cause there, not the cable. From https://www.keysight.com/main/editorial.jspx?cc=US&lc=eng&ckey=1428419&nid=-32775.536879654&id=1428419
The 4294A extends its measurement frequency range up to 110 MHz by terminating each measurement terminal with 50 ohm in order to eliminate the resonance of test leads (including leads inside the 4294A). The measurement discontinuity is caused by the change in termination impedance at 15 MHz when the ADAPTER is set to NONE or at 5 MHz when it is set to 1m or 2m. The measurement discontinuity can be removed by performing LOAD compensation.
Something as simple as a cable does not have discontinuities like that.
There may be a clue in the fact the problem occurs at a nice round number, 5MHz. Is this a place where your test set changes ranges? Maybe it changes output amplifier, or filter, and one of them is broken or damaged.
The fact that you've quoted measurements at 4.99MHz and 5.01MHz without listing them hints that you have more data hidden that might throw light on what's going on. Listing spot measurements at a few selected frequencies is fine when everything is behaving itself, but not when you're hunting for an anomaly. The detail of the response adjacent to 5MHz will be very valuable.
Please edit your question with a plot of all the data you have taken, which may allow us to make better guesses. A connection schematic to show exactly how the cable is connected to the analyser would be useful as well.
The effect you have observed has nothing to do with transmission lines. You need to consider 'skin effect'. You'll find it in any good RF textbook, such as Terman, Radio Engineering. Basically, as the frequency increases, the main current flow moves further from the conductor's centre, ie, the current flows in the skin of the conductor. The higher the frequency, the smaller the skin's cross-sectional area, and hence, the higher the resistance. To a first approximation, the current carrying area is inversely proportional to the square root of the frequency. This explanation covers your first 6 data points, but the 7th is more likely to be a resonance effect related to your measurement technique. It would also help to identify your units of frequency.
Consider the cable (I assume coax) as a string of small inductors with capacitors at the junction of each pair of inductors to ground (the shield). At low frequencies the inductors act as they would with near DC signals (a wire) and the capacitors would be near opens at the near DC signals.
As the frequency goes up the inductors have more reactance and the capacitors have lower impedance, eventually forming effectively a series of LC filter poles. At some frequency the combined filter characteristics will become pronounced, especially with an unterminated (50-75 Ohms) line. Add the correct termination resistance and things should look a lot better behaved. Most coax cables do have an upper limit of usefulness due to the inter electrode capacitance.
