Rooms furnished entirely from one period are rare outside museums, and they tend to feel like it. Almost every interior worth looking at is a mixture, and the difficulty is that mixing badly is far easier than mixing well.
The usual advice is to combine old and new for contrast, which is true and useless. Contrast is not the mechanism. What actually holds a mixed room together is a small number of shared properties running underneath the differences.
Match one thing, vary the rest
Pieces from different centuries will sit together if they agree about something. It only needs to be one property, held consistently.
It might be tone, so that everything in the room is mid-dark regardless of age. It might be material, a room where everything is timber, linen or stone and nothing is plastic or chrome. It might be a line, a preference for straight legs and square edges that a Georgian chair and a modern sofa can both satisfy.
Rooms that fail usually agree about nothing. Rooms that feel flat agree about everything.
Respect the weight
Antique furniture is almost always visually heavier than modern furniture. It has thicker sections, sits closer to the floor and is made of denser material. Put a carved Victorian chest next to a slim contemporary sofa and the chest wins, and the sofa reads as temporary.
The fix is to balance across the room rather than within a pairing. Give the heavy piece a wall of its own and put visual weight of a different kind opposite, a large picture, a dark curtain, a deep rug. The room then reads as balanced even though nothing in it matches.
One period should lead
An even split reads as indecision. If roughly seventy per cent of a room belongs to one period and the rest is introduced against it, the minority pieces read as deliberate choices. At fifty-fifty they read as whatever was available.
This is also the cheaper approach, because it means you are looking for two or three good things rather than furnishing twice.
Be careful with the obvious pairings
Certain combinations have been used so heavily that they now read as a style rather than a choice. The industrial workbench with the crystal chandelier. The gilt mirror over the concrete fireplace. The single mid-century chair placed in the corner of an otherwise period room.
None of them are wrong, but they no longer say anything. If a pairing was the point of the room, it needs to be a pairing you arrived at rather than one you recognised.
Let the new things be plain
The most reliable version of this is to let the old pieces carry the character and keep the new ones quiet. Modern upholstery in undyed linen, plain shelving, simple lighting. The contemporary elements then function as the neutral ground that lets an old object be looked at properly.
Reverse it, with an elaborate modern piece and a plain antique, and the antique simply looks like something nobody got around to replacing.