diff --git a/tests/unittests/text/test_bertscore.py b/tests/unittests/text/test_bertscore.py
index dfd6d60a0e5..28668c66b54 100644
--- a/tests/unittests/text/test_bertscore.py
+++ b/tests/unittests/text/test_bertscore.py
@@ -13,6 +13,7 @@
 # limitations under the License.
 import os
 from functools import partial
+from itertools import product
 from typing import Sequence
 
 import pytest
@@ -190,4 +191,103 @@ def test_bertscore_sorting(idf: bool):
     score = metric(preds, targets)
 
     # First index should be the self-comparison - sorting by length should not shuffle this
+
+@skip_on_connection_issues()
+@pytest.mark.skipif(not _TRANSFORMERS_GREATER_EQUAL_4_4, reason="test requires transformers>4.4")
+@pytest.mark.parametrize(
+    ["idf", "batch_size"],
+    [(False, 1),
+     (False, 9),
+     (True, 1),
+     (True, 9)],
+)
+def test_bertscore_most_similar(idf: bool, batch_size: int):
+    """Tests that BERTScore actually gives the highest score to self-similarity."""
+    short = "hello there"
+    long = "master kenobi"
+    longer = "general kenobi"
+    
+    sentences = [short, long, longer]
+    preds, targets = list(zip(*list(product(sentences,
+                                            sentences))))
+    score = bert_score(preds, targets, idf=idf, lang="en",
+                       rescale_with_baseline=False, batch_size=batch_size)
+    for i in range(len(preds)):
+        max_pred = i%(len(sentences))*(1 + len(sentences))
+        max_target = int(i/(len(sentences)))*(1 + len(sentences))
+        assert score["f1"][i] <= score["f1"][max_pred], \
+            f"pair: {preds[i], targets[i]} does not have a lower score than {preds[max_pred], targets[max_pred]}\n{i=}{max_pred=}"
+        assert score["f1"][i] <= score["f1"][max_target], \
+            f"pair: {preds[i], targets[i]} does not have a lower score than {preds[max_target], targets[max_target]}\n{i=}{max_target=}"
+
+
+
+@skip_on_connection_issues()
+@pytest.mark.skipif(not _TRANSFORMERS_GREATER_EQUAL_4_4, reason="test requires transformers>4.4")
+@pytest.mark.parametrize(
+    ["idf", "batch_size"],
+    [(False, 1),
+     (False, 9),
+     (True, 1),
+     (True, 9)],
+)
+def test_bertscore_symmetry(idf: bool, batch_size: int):
+    """Tests that BERTscore F1 score is symmetric between reference and prediction.
+    As F1 is symmetric, it should also be symmetric."""
+
+    short = "hello there"
+    long = "master kenobi"
+    longer = "general kenobi"
+
+    sentences = [short, long, longer]
+    preds, targets = list(zip(*list(product(sentences,
+                                            sentences))))
+    score = bert_score(preds, targets, idf=idf, lang="en",
+                       rescale_with_baseline=False, batch_size=batch_size)
+    for i in range(len(preds)):
+        for j in range(len(targets)):
+            if preds[i] == targets[j] and preds[j] == targets[i]:
+                assert score['f1'][i] == pytest.approx(score['f1'][j]), \
+                    f"f1 score for {(preds[i], targets[i])} is not the same as {(preds[j], targets[j])}."
+    pass
+
+        
+@skip_on_connection_issues()
+@pytest.mark.skipif(not _TRANSFORMERS_GREATER_EQUAL_4_4, reason="test requires transformers>4.4")
+@pytest.mark.parametrize(
+    ["idf", "batch_size"],
+    [(False, 1),
+     (False, 3)]
+)
+def test_bertscore_additional_sentence(idf: bool, batch_size: int):
+    """Tests that BERTscore keeps the same scores for previous inputs
+    by adding additional elements to the input lists. This should be the case for idf=False."""
+
+    short = "hello there"
+    long = "master kenobi"
+    longer = "general kenobi"
+
+    preds = [long,long]
+    targets = [long,short]
+
+    score = bert_score(preds, targets, idf=idf, lang="en",
+                       rescale_with_baseline=False, batch_size=batch_size)
+
+    longlong = score["f1"][0]
+    longshort = score["f1"][1]
+    # First index should be the self-comparison - sorting by length should not shuffle this
+    assert longlong > longshort
+    
+    preds = preds + [short, longer]
+    targets = targets + [longer, long]
+
+    score = bert_score(preds, targets, idf=idf, lang="en",
+                       rescale_with_baseline=False, batch_size=batch_size)
+
+    # First two indices should be exactly as in the previous call to metric
+    assert score["f1"][0] == pytest.approx(longlong)
+    assert score["f1"][1] == pytest.approx(longshort)
+    # Indices 1 and 2 should also be smaller than self-comparison.
     assert score["f1"][0] > score["f1"][1]
+    assert score["f1"][0] > score["f1"][2]
+