Also, just read the parts where Bashir is possessed, below . . . don't watch the episode. Siddig read those lines horribly . . . seriously, it was like he had been stunned.
1. The tractor beam caught a shielded ship.BASHIR: It was necessary to render him unconscious for the time being. However, I might consider leaving his body and returning him to you. But first you must release your tractor beam.
SISKO [on viewscreen]: I can't do that.
BASHIR: If you don't, I'll take this vessel to warp.
[Ops]
SISKO: The tractor beam would rip apart your ship, and you and everyone on board would be killed.
BASHIR [on viewscreen]: Exactly. So if you care at all about the welfare of your Doctor, you will release your hold on us. You have one minute to decide.
(Transmission ends)
SISKO: Can we get a transporter lock on him?
PRIMMIN: Negative. Their shields are up.
SISKO: Suggestions?
KIRA: A small ship like a runabout might be able to get close enough to overload their shield generators with directed phaser fire. We used to do it to Cardassian freighters all the time.
ODO: But you'd be risking a hull breach and with all the deuridium on board
SISKO: He's right. We can't risk releasing deuridium into the system. Every populated area would have to be evacuated. Dax, is there any way to disrupt Vantika's control over Bashir?
DAX: I have an exact model of Vantika's neural energy patterns. If I can design an electromagnetic pulse to disrupt those patterns, Julian might emerge. We still need a way to get it there.
SISKO: Could we run it right along the tractor beam at the same frequency as their shields?
DAX: The pulse would resonate off the shields and create a reflected EM field inside the ship.
Ideally, here, they should've used the concept of a transport scrambler rather than shields, because the only reason they needed shields was to prevent transporter function. A line of dialog like "and if you try to shoot at this ship I'll take it to warp" would've helped serve to prevent them from firing.
2. A tractor beam (at least on a shielded ship, though it isn't clear if that's relevant) prevents the use of warp drive but only in the sense that you'll blow yourself to kingdom come in the process.
Indeed, I wonder if this was actually Riker's plan in BoBW right before Data saved the day . . . my mental picture here is that you'll actually achieve forward velocity, but you'll be torn apart. In theory, then, it would be kind of like turning yourself into a shotgun as you blast your shrapnel in the direction of travel. In the case of BoBW, they'd have been using the Enterprise-D as a shotgun against the cube . . . still a ramming attack, sort of, but a very much more untidy version.
In any case, I seem to recall another instance of a tractor beam being used to prevent a ship from going to warp, but I can't put my finger on it right now. I thought it did something to the subspace field, though. I may simply be thinking of the inverse graviton burst from "Once More Unto the Breach", which was a somewhat different thing that came from the main deflector.
3. Extreme short range phaser fire can be used to overload the shield generators of ships. Whether this is just a straight power thing (implying phaser power falls off at a distance rather severely) or a super-spiffy targeting thing or some sort of technobabble is not clear. But, this may have some sort of relevance to the shorter ranges often, but not always, seen in later Trek.
4. A tractor beam can be used, via technobabble, to produce electromagnetic pulse effects within a shielded opposing vessel.
5. Having or figuring the shield frequencies to make the EM pulse reflect-o-matic thingy work was not the same thing as being able to fire phasers or transport through the shields, otherwise they could've just shot up the freighter or beamed Slow-Talkin'-Bashir out.
Then we have this:
This is the one where they engage a Cardassian transporter on Julian's head, which looks like it's gonna be some sort of savage high-tech decapitation until the head's still there when the transporter stops. Instead, they beamed out some intruding cells which they were able to identify with sensors.DAX: I've programmed this transporter to isolate any glial cells with Vantika's neural patterns and to beam them from Julian into this micro-containment field. Once they're out he should be back to normal.
(The container starts blinking)
DAX: I'm only reading human neural patterns. He's clear.
(Dax gives Bashir a hypo to wake him)
BASHIR: I have the worst headache.
That's a super-cure to end all super-cures that they apparently realized they should never use again. I mean, you can cure virtually anything with that. The whole plot of "Shades of Grey"[TNG2] would be meaningless . . . well, moreso than it already was. Even the Holodoc never tried anything quite so brazen, even when it would've been very useful in curing Ensign Kim when the 8472 cells were consuming him.