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In the 2009 film,
The Enterprise ejects and detonates its warp cores in an attempt to close a massive singularity. They maintain warp speed in order to attempt to escape the gravitational pull of the singularity.
How did the Enterprise maintain warp despite having ejected its cores?
Just as a photon torpedo is able to maintain warp flight using a warp sustainer engine (even though it has no warp core itself), so too should a ship be able to sustain a warp field on auxiliary power for some time after a warp core is no longer present/active. Here is the relevant excerpt from the photon torpedo entry on Memory Alpha, taken from the Star Trek: The Next Generation Technical Manual:
The propulsion system of the torpedoes is a warp sustainer engine. The engine coils of the torpedo grab and hold a hand-off field from the launcher tube's sequential field induction coils. A miniature matter/antimatter fuel cell adds power to the hand-off field. When launched in warp flight, torpedo will continue to travel at warp, when launched at sublight, torpedo will travel at a high sublight speed, but will not cross the warp threshold. (pg. 129)
As Kalamane points out in a comment, the ability to maintain a warp field without a warp core has been referenced before in the TNG episode "Brothers". The excerpt from the script:
PICARD: Mister La Forge, prepare for saucer separation.
WESLEY: Sir, we're at Warp nine three.
PICARD: I am aware of the risks, Ensign. When the umbilical splits, we should regain primary control, do you agree?
LAFORGE: Yes, sir.
PICARD: The saucer module should fall out of warp in two minutes. Be prepared to sweep back. Pull it in with a tractor beam.
If the warp-core-less saucer section has enough power to maintain a hand-off warp field from the secondary hull for a couple of minutes, then a whole ship that has lost its warp core should be able to do the same.
A "Warp Core" is just the label given to the matter-antimatter reactor on most starships. A starship can technically be warp-capable without a warp core so long as it has some other energy source to power the warp coils, which are the mechanisms which actually generate the warp bubble and allow the ship to travel at warp speeds.
So a simple in-universe explanation would be that the warp core was ejected, but the ship still had enough reserve energy (either in batteries/energy banks/residual drive plasma that remained in the EPS) to maintain a warp bubble for however long it was.
Also, a warp bubble could be a self-sustaining phenomenon.
Newton's 1st law of motion states that a body in motion will stay in motion until an outside force act upon it. I would assume that they were traveling that fast and nothing was causing it to stop being at warp immediately, so the ship would keep it's velocity constant until an outside force (gravity from another mass, the ship stopping itself, etc) caused it to stop.
After the field coils have been de-energized, a residual field will remain and decay.
They are similar to an electro-magnet in this regard.
As magnets produce their own magnetic field, I suspect that warp field coils naturally produce their own subspace field, which the electro-plasma amplifies.
Warp drive is a non-Newtonian propulsion method. TNG Technical Manual page 54. Reaction products are channelled into field coils, producing layers of energy that push on each other, pushing the ship into subspace and propelling the ship faster than light.
According to the TNG Technical Manual page 28, "Decaying warp field energy surrounding the saucer module is managed by the driver coil segments of the impulse engines. This energy will take, on average, two minutes to dissipate and bring the vehicle to its original sublight velocity."
Subspace also imparts drag upon a ship, one of the reasons ships are built with sweeping curves. Subspace though like space, is also a medium containing layers. Each successive layer can require thousands of times the energy needed to travel in a previous layer.
Like everyone said above, the warp bubble is separated due to the remaining energy left from the warp core loss in the power conduits.
Think about it like a real life bubble, you have two bubbles after one splits until they both eventually pop or fly away. Yet in VOY: Day of honor, whenvoyager lost its warp core it immediately dropped out of warp a few seconds after.
Warp fields, warp bubbles and spatial distortions are used to accelerate to warp speeds. The warp field and bubble allows the ship to "surf" the distortions to FTL (faster than light) speeds. To maintain warp speed, all you have to do is maintain a warp field and bubble, plus the spatial distortions with a warp sustainer engine. Same way a photon torpedo warps out of the tubes. Warp bubbles can hold their shape longer on its on WITHOUT any external energy.
You definitely have to take into consideration the fact that they were trying to escape at maximum warp based on their technology. Trying to maintain maximum warp without a warp core is just like trying to power a coffee maker with a 500va backup battery. The amount of time you can sustain warp field in addition to the "push" you would get from a warp core ejection detonation is not substantial enough to allow escape from a singularity of that magnitude. Based on the magnitude of the "red" matter used on Vulcan, the amount released during this battle would have either had a longer effect or a greater magnitude. In either situation, a warp core detonation and warp core bubble being sustained by what little power the ship had left would not have sufficed to allow the Enterprise escape. It would have been much better if they included the detonation of the warp core of the Narada into the sequence...THAT would have been more believable to us "old guards".
I believe they return to Starbase 001 off of the acceleration that was applied to the Enterprise during the resulting antimatter explosion, and also Impulse engines and thrusters... it'd take a long ass time to get back but, hey, they'd get back eventually.
An object in motion will stay in motion until acted upon by an outside force. There is little to no force in space so the Enterprise should not have slowed to a stop at least for a good bit of time
