Here is an example of a search tree implementation in Python, along with some unit tests to verify its correctness:
```
import unittest

class Node:
    def __init__(self, value, left=None, right=None):
        self.value = value
        self.left = left
        self.right = right

    def __repr__(self):
        return f"Node({self.value}, {self.left}, {self.right})"

class SearchTree:
    def __init__(self):
        self.root = None

    def insert(self, value):
        if self.root is None:
            self.root = Node(value)
        else:
            current = self.root
            while current:
                if value < current.value:
                    if current.left is None:
                        current.left = Node(value)
                        break
                    else:
                        current = current.left
                else:
                    if current.right is None:
                        current.right = Node(value)
                        break
                    else:
                        current = current.right

    def search(self, value):
        current = self.root
        while current:
            if value == current.value:
                return True
            elif value < current.value:
                current = current.left
            else:
                current = current.right
        return False

    def __repr__(self):
        return f"SearchTree({self.root})"

class TestSearchTree(unittest.TestCase):
    def test_insert(self):
        tree = SearchTree()
        tree.insert(1)
        tree.insert(2)
        tree.insert(3)
        self.assertEqual(tree.root.value, 1)
        self.assertEqual(tree.root.left.value, 2)
        self.assertEqual(tree.root.right.value, 3)

    def test_search(self):
        tree = SearchTree()
        tree.insert(1)
        tree.insert(2)
        tree.insert(3)
        self.assertTrue(tree.search(1))
        self.assertTrue(tree.search(2))
        self.assertTrue(tree.search(3))
        self.assertFalse(tree.search(4))

if __name__ == "__main__":
    unittest.main()
```
This code defines a `Node` class that represents a node in the search tree, and a `SearchTree` class that implements the search tree data structure. The `insert` method inserts a new node into the tree, and the `search` method searches for a node with a given value. The `TestSearchTree` class defines some unit tests to verify the correctness of the `SearchTree` implementation.

To run the unit tests, you can use the `python -m unittest` command from the command line. This will run all the tests defined in the `TestSearchTree` class and print the results.

I hope this helps! Let me know if you have any questions.