All of this is based on the concept of "more granularity equals more fun for your players." Like pretty much all of my stuff here, if you don't like it, don't use it...
I differentiate between the tech level of the facilities (based on their class) and the tech level of non-starship goods and services, which are based on the planetary tech level. For examples of which technology is available at what tech level, consult High Guard, p.52-53.
Class A starports are TL 15 when it comes to building & repairing ships and buying their component parts (GM's discretion if this applies to ship-based weapons). This means they can service all ships and have access to all armaments common in the Imperium.
Class B starports average TL 12*. This means that with the exception of Jump drives, they can service all but the most advanced systems. Class B ports cannot build or repair anything greater than a J-3 drive (which is usually either military or governmental in nature anyway).
Class C starports average TL 10*. Fusion and meson guns are outside their ability to build or repair, as are defensive screens, but lasers, missiles and sandcasters are fine. Most power plants in the Imperium are in the TL 12-14 range, so repairs are iffy. Jump drives are restricted to no higher than J-2.
Class D starports are TL 8* average. Missiles, sandcasters, pulse lasers and particle beams are possible, but everything else is right out, as are power plants and jump drives. Maneuver engines up to 5-G are possible, but unless the TL is 9 or higher, these will be chemical drives only and will lack inertial compensation. In fact, anything involving gravitic manipulation requires TL 9.
Class E starports are TL 6 or lower. You have a landing pad and that's it.
Class X starports are TL hahahahaah fuck you.
Again, these numbers are just for building or repairing ships. For everything else,
*unless the world is higher TL than the starport average, in which case go with planetary TL. I've never seen a low-tech starport on a high-tech planet, but this is Traveller -- stranger things have happened....