No thrust, so that leaves out things like the EMDrive. Not wanting gas filled ships leaves out any sort of buoyancy based hovering. We're left with one choice, actual anti-gravity.
The problem with any sort of science-based anti-gravity device is to produce it we need negative mass to produce negative gravity. More precisely, we need to curve space-time in the opposite direction of gravity... we need an energy density lower than that of a vacuum. Fortunately for you, gravity is not well integrated into other physical theories (the famous lack of a theory of quantum gravity) leaving you some wiggle room.
Traditionally negative mass is impossible, but work on the Alcubierre Warp Drive has shown it might be possible and consistent with some theories. Again, it's not so much negative mass as an energy density lower than that of vacuum which produces a negative pressure, like in air. The Casimir effect is one candidate and various unconfirmed forms of exotic matter are another.
If you think of gravity as a curved slope heading down towards the Earth, negative mass would allow you to make a little ledge for your ship to sit on. This counteracts not just the ship's own attraction to the Earth, but the far larger Earth's attraction to the ship. This would require a lot of energy. Unfortunately that is beyond my abilities to exactly calculate, but we can get an idea by looking at the gravitational force. Take HMS Dreadnought at 18,000 tonnes (go big or go home). The gravitational force alone is 1.8 x 108 N which is about 14 Space Shuttle boosters.
So you're going to need a massive energy source to power your negative energy pressure field.
The other option is something something something DARK ENERGY!!!
Currently, Dark Energy is an unknown force which is accelerating the expansion of the universe. It does this by providing a negative energy pressure to all of space-time... our anti-gravity!
Since we don't know what Dark Energy is, the exotic matter mentioned above is one candidate, and because it's everywhere it's within the realm of sci-fi to propose somebody figured out how to harvest, store and manipulate it.
The good news is it's probably everywhere. The bad news is it's probably evenly spread out over the whole universe so there's not a lot of it anywhere. Current theory puts it at 7x10−30 g/cm3 equivalent mass-energy. That means in the whole volume of the Earth there's the equivalent of 7.5 mg of Dark Energy. To float a person we'd need 100 kg or about 15,000,000 times more. To float a battleship we need 18,000,000 kg.
In your story you'd need a plausible reason why there's suddenly a lot of dark energy available to a Victorian society.
Finally, I would be remiss not to mention the fictional Element Zero from the video game Mass Effect. This is a substance produced by a star going supernova. When you pass electricity through it, it produces Dark Energy which is manipulated into the titular "mass effect field" which can raise and lower the mass of objects.
Element Zero is used to explain all the apparently magical effects in this science-fantasy game. FTL travel, armor, weapons, levitation, and even psionic abilities are all explained in terms of raising or lowering an object's mass.
I would recommend playing the first Mass Effect to get ideas, and it's a very good game.