Orange Microdark. When you plug headphones into the headphone jack, you get cabinet emulation and do not require a load on the cab out. There is no standby on this little wonder of an amp (frankly for the money I don't think you can get a better amp of this class), you just plug in the headphones and you're good for silent practice/recording. This amp is an EXCELLENT (!!!) choice for this purpose (and it sounds great).
Hugh and Kettner Tubemeister: Very smart amp, has onboard attenuator. You put it on standby and set the attenuator to "silent" and use the emulated out (which is not a headphone jack, it's meant for running to a PA or interface etc) and you do not require a cab/load. There is no headphone jack. Excellent amp for the silent recording/practicing purpose, but pricey.
Marshall JVM410h: Allegedly, if the presence and master volumes are at 0 and you are in standby, the power amp is not engaged (or at least, is engaged so minimally no damage is done), and you are fine to use the cabinet-emulated out or preamp send for silent recording. There is no headphone jack. This monster is a great amp, but very expensive and way, way more horse than you'd need unless you're playing a mid/large sized venue.
Every single one of them has an emulatedspeaker-emulated out. I run that into an interface (like a Scarlett or some such) and use the headphone jack on the interface. This lets me dial up the amp hard, but cut the gain going into the headphones by using the gain control on the interface. You can get any tone you want.
On the Marshall, for silent recording, I run my guitar into a Helix, run a send out of the Helix into the guitar input of the amp, run the parallel send of the amp back into the Helix receive, and on the Helix put a cabinet model in the path. I can then use the headphone jack on the Helix. Alternatively, I run the emulated out into an interface and again just use the headphone jack on the interface.
On the Randall, the same as the marshall; parallel send, or emulated out, into interface of some kind, use the headphone jack on the interface.
On any of the above, it is ALWAYS recommended to run a cab or load box on the cab out, even if the manufacturer says it's ok not to. This isn't so much because you don't believe them, it's because it only takes an unnoticed bump on a master volume, or an accidental flip of the standby, or (in the microdark) you unplug your headphones and forget to turn the amp off, to blow a tube amp that doesn't have anywhere to send the load. And again, some amps simply can't be run without a cab/load box under any circumstances.
To that end, getting a load box for people that want to use tube amps for silent recording/practice is a VERY GOOD IDEA. I have a Rivera load box that also acts as a cabinet emulator. You plug your cab out into the load box, pick the cabinet emulation you want, and either use the headphone jack on the Rivera, or run the Rivera out to an interface that has a headphone jack. The load box can eat the whole load of the power amp, so you can run your amp REALLY hot, dial back the output on the load box, and get a full-on tube signal. This is a standard in studios.
Total disclosure, I am not a pro amp tech. But I've been around them a long time and, know some guys that are really knowledgeable, I'm really careful with my research but still made a lotsome of the rookie mistakes, and this really sounds like one of them. I would be willing to bet some money that if you asked the amp manufacturer "headphones into power amp out", there'd be a pause on the phone, followed by, "...you want to do what?"