Proving to someone else the knowledge of a secret without revealing any of its information is an interesting feature in cryptography. The best solution to solve this problem is a Zero-Knowledge Proof (ZKP) protocol. Nurimisaki is a Nikoli puzzle. The goal of this game is to draw a kind of abstract painting ("Nuri") that represents a sea with some capes ("Misaki") of an island (represented by white cells). For this, the player has to fulfill cells of a grid in black (representing the sea) in order to draw some capes while respecting some simple rules. One of the specificity of the rules of this game is that every "Misaki" cell can only have one white neighbour. Kurodoko is also a Nikoli puzzle where some cells need to be blackened in order to ensure that each numbered cell is surrounded by the same number of white cells in the four directions (north, east, south, and west). Both of these puzzles, Nurimisaki and Kurodoko, share a common connectivity constraint. Using a deck of cards, we propose a physical ZKP protocol for each of the two puzzles above. Our protocols prove that a player knows a solution of (1) a Nurimisaki grid, or (2) a Kurodoko grid, without revealing any information about the solution.