Romulan warbirds and klingon bird of preys (as well as federation ships) are made of materials absolutely unknown today and we don't know the properties of that materials. Furthermore, we don't know much about their engines and what kind of radiation they would emit. And all we know about their sensor technology is that it's really fancy. So, let's stay in our century.
In principle, a submarine does not emit anything that allow to locate it from a larger distance. The only methods so far are sonar, and listening to noise from the submarine, and measuring the distortion of the magnetic field by this large piece of metal in the ocean. The first two options work under water and close proximity only, the third can be used by deep flying aircraft, but still works for low distances only. :-(
You mentioned radioactive stuff. Most people know α, β and γ radiation. It is also known that the first two can be shielded easily (and completely) by a thin layer of metal, while γ radiation needs more care. Typically, thick shields of lead or similar heavy materials are used to drop the radiation level down to a value comparable to the level of the environment. (But this is to protect the staff!) Furthermore, water isn't the best shielding material, but the thickness of the water layer above the submarine compensates this. So, no chance to detect this. :-(
Well, α, β and γ radiation aren't the only types, there are more.
Neutrons play a key role in nuclear reactors, but can easily be shielded - and it turns out water is the best material. :-(
When a β-decay occurrs, not only a β-particle (an electron) escapes from the nucleus, but also an anti-neutrino . The interesting fact is that (anti-)neutrinos can not be shielded: You would need a stack of lead as thick as the diameter of earths orbit around the sun to catch just 50% of the neutrinos...
A 1GW nuclear power plant releases about $10^{21}$ anti-neutrinos per second. It will be less for a submarine, but this is a number I found, and it can easily be scaled down.
This number seems to be large, but in a distance of 1km, this leads to a flux of $8\cdot10^9$ anti-neutrinos per cm² and second. For comparison: The sun emits large amounts of neutrinos, the flux here is $6\cdot10^{10}$ per cm² and s on earth. (Keep in mind: sun: neutrinos. Reactor: anti-neutrinos)
On Saturn, the flux from our reactor is just about $3\cdot10^{-9}$ per cm² and s (or 1 anti-neutrino per squaremeter and 10 hours), while the flux from the sun is just 1/100 of the value on earth, i.e. $6\cdot10^8$ per cm² and s.
An observer on Saturn needs a large detector and a lot of time to get enough neutrinos. AND he somehow hast to distinguish all the different submarines and power plants, as well as the natural radiation of the earth. :-/
Now, the initial advantage of neutrinos of extreme rare interaction with matter becomes a disadvantage. These interactions are also what a sensor measures. This means you need a really really vast sensor volume and a really really long observation time to observe just a really really tiny fraction of all the anti-neutrinos flowing through this volume. :-(
Next, the path (origin) of low energy anti-neutrinos as emitted by radioactive processes can not be determined, so distinguishing between several submarines is not possible. :-(
By the way: There have been ideas to use large supertankers filled with a liquid detector material to discover nuclear power plants. Those would be sent to the coast of a suspicious country to check if they have nuclear power plants. But that's just an idea to my knowledge, and I don't know how they should work. I guess, they would measure the rate only.
Finally, it is not possible to detect a nuclear driven submarine from saturn today. Even if we assume that in the future we will be able to detect EACH anti-neutrino as well as its origin, the flow from earth on saturn is so low that we still need much observation time and vast detectors. At least, it might be possible to detect that there is an anti-neutrino source somewhere in space, which would be enough to detect a cloaked submarine in space...
