This is a bit challenging problem. Once I struggled a lot to find out how to solve a Separated Head from the Body (the Neck was cut off, near the Head Joint).
First: The Weight Paint affecting both Meshes, must be exact. It would be as if one were Weight Painting Ratios on a single Mesh Object.
Thus, if one has got a Head Bone and a Neck Bone, the same Bones, for sure, can be reused for the Weight Paint on both Mesh Objects, but the Blended Weights (Ratios) must be exactly the same on both Meshes, in respect to the Deform Bones which are affecting both Meshes.
Note: there would be different approach to reach the exactitude here. If there are very few Vertices, one easy approach is just to set manually one by one, matching values gradually.
Second: It’s probably necessary that many impactful Modifiers must also be equal, for both Meshes. Something is very likely to go wrong, if there are any substantial difference between, from one Mesh Object to the other, let’s say, their Armature Modifiers (e.g., one has got Preserve Volume Option on, the other off), or their Subdivision Surface Modifiers (e.g., different Levels of auto-Subdivisions).
Third: if the Mesh is Low-Poly, or very Low-Poly, the Meshes in the connecting Edge Ring won’t look seaminless. To my experience. Thus, more real Subdivisions (on Edit Mode for both Mesh Objects), a higher Mesh Density there therefore, is usually a good idea. I just don’t remember if only a few extra Transversal Edge Rings (wristwatch-like, bracers-like circular orientation around the Limb) will do closest to the Connecting Region, or only a few extra Aligned Loop Cuts with the Limb direction will do, or, it would be needed to cross both Transversal and Aligned Loop Cuts in order to suppress Low-Poly bad visual seaming in Render Preview (I believe it’s the first case). It is likely, a few of Subdivisions alone from Subdivision Surface Modifier should also be an alternative, for the whole Mesh Objects, since it’s a visual problem of Low-Poly lacking Subdivisions glitch, it’s not a structural thing (I believe). However, with the real Subdivisions on a very specific Mesh Region, it’s way more economic than having to give Modifie Subdivisions to the whole Meshes all at once (it’s a waste; unless it would be required for solving other problems of the Model, and simultaneously it solves the Connecting Region glitch problem).
Fourth: Do make sure the feature of Shade Smooth or Auto Smooth, is the same for both Mesh Objects. The former may be accessed from RMB-Click on a Mesh Object on Object Mode, and the latter from the Properties Editor. If Auto-Smooth is being used… it should be safe if its settings are the same for both Mesh Objects… but can never be sure; if it doesn’t work, try pure Smooth for both.