diff --git a/src/uproot/const.py b/src/uproot/const.py
index a4a1feeca..798c03fd5 100644
--- a/src/uproot/const.py
+++ b/src/uproot/const.py
@@ -12,6 +12,8 @@
 # determines when a file is "big"
 kStartBigFile = 2000000000
 
+kMaxTBasketBytes = numpy.iinfo(numpy.int32).max
+
 # used in unmarshaling
 kByteCountMask = numpy.int64(0x40000000)
 kByteCountVMask = numpy.int64(0x4000)
diff --git a/src/uproot/writing/_cascadetree.py b/src/uproot/writing/_cascadetree.py
index 6019af610..7df7a85e7 100644
--- a/src/uproot/writing/_cascadetree.py
+++ b/src/uproot/writing/_cascadetree.py
@@ -1395,6 +1395,13 @@ def write_np_basket(self, sink, branch_name, compression, array):
         fObjlen = len(uncompressed_data)
         fNbytes = fKeylen + len(compressed_data)
 
+        if max(fObjlen, fNbytes) > uproot.const.kMaxTBasketBytes:
+            raise ValueError(
+                f"Numpy array data of branch {branch_name} has an uncompressed size of {fObjlen} bytes "
+                f"and a compressed size of {fNbytes} bytes, which is too large to fit in a TBasket. "
+                "Neither of these sizes can exceed 2 GiB."
+            )
+
         parent_location = self._directory.key.location  # FIXME: is this correct?
 
         location = self._freesegments.allocate(fNbytes, dry_run=False)
@@ -1470,6 +1477,13 @@ def write_jagged_basket(self, sink, branch_name, compression, array, offsets):
         fObjlen = len(uncompressed_data)
         fNbytes = fKeylen + len(compressed_data)
 
+        if max(fObjlen, fNbytes) > uproot.const.kMaxTBasketBytes:
+            raise ValueError(
+                f"Jagged array data of branch {branch_name} has an uncompressed size of {fObjlen} bytes "
+                f"and a compressed size of {fNbytes} bytes, which is too large to fit in a TBasket. "
+                "Neither of these sizes can exceed 2 GiB."
+            )
+
         parent_location = self._directory.key.location  # FIXME: is this correct?
 
         location = self._freesegments.allocate(fNbytes, dry_run=False)
@@ -1559,6 +1573,13 @@ def write_string_basket(self, sink, branch_name, compression, array, offsets):
         fObjlen = len(uncompressed_data)
         fNbytes = fKeylen + len(compressed_data)
 
+        if max(fObjlen, fNbytes) > uproot.const.kMaxTBasketBytes:
+            raise ValueError(
+                f"String data of branch {branch_name} has an uncompressed size of {fObjlen} bytes "
+                f"and a compressed size of {fNbytes} bytes, which is too large to fit in a TBasket. "
+                "Neither of these sizes can exceed 2 GiB."
+            )
+
         parent_location = self._directory.key.location  # FIXME: is this correct?
 
         location = self._freesegments.allocate(fNbytes, dry_run=False)