The best platformer games like Castlevania are Super Castlevania IV, Castlevania Symphony of the Night and Ghosts n Goblins. Below are 9, each with the reason it is here — and, at the end, what filtering to platformer costs you.
Filtering to platformer means you want the movement itself to be the pleasure. It is the right filter when the thing you liked was getting from one place to another.
What you get: A game you can judge in ten seconds. Platformers live or die on the jump, and a good one feels right before anything else happens.
What made Castlevania worth playing in the first place is covered on the full list. This page is the platformer part of that answer, and only the platformer part.
The same game loosened up — whip in eight directions, and the atmosphere intact.
Where the series stopped being stages and became a map. The other half of the genre.
The same era of unforgiving, pattern-learned platforming.
The other NES action platformer built on memorising a level until it becomes easy.
Faster, meaner, and the wall-climbing gives you options Simon never had.
The modern continuation, made by the producer of Symphony of the Night.
Heavy, punishing, religiously ornate — the tone taken seriously.
If the map rather than the stages is the part you want.
NES platforming rebuilt with everything learned since, Castlevania included.
Weight. Platformers rarely carry a story you will think about afterwards, and the collectible-led ones can become checklists if you let them.
Specifically, these are strong answers for Castlevania that are not platformer games, so they are not on this page:
The full list is on games like Castlevania — 10 picks, no genre filter.
Super Castlevania IV. The same game loosened up — whip in eight directions, and the atmosphere intact.
No. Castlevania released on the Nintendo Entertainment System, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Whether the move set is complete early. The great ones give you everything in the first level and spend the rest asking better questions of it; the weak ones drip-feed abilities to disguise thin level design.
Different games. 2D platformers are about precision on a single screen; 3D ones are about reading space and camera. Each pick below says which it is.
By hand. Each pick was written for the full Castlevania list first, on what the game actually does, and this page is the part of that list that is platformer — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the platformer guide for where to start in the genre generally.