diff --git a/tests/compat.sh b/tests/compat.sh
index 0eae1eab3..80c2d31a3 100755
--- a/tests/compat.sh
+++ b/tests/compat.sh
@@ -15,6 +15,10 @@
 
 set -u
 
+# Limit the size of each log to 10 GiB, in case of failures with this script
+# where it may output seemingly unlimited length error logs.
+ulimit -f 20971520
+
 # initialise counters
 TESTS=0
 FAILED=0
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index f54295b6e..ed97f233f 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -21,6 +21,10 @@
 
 set -u
 
+# Limit the size of each log to 10 GiB, in case of failures with this script
+# where it may output seemingly unlimited length error logs.
+ulimit -f 20971520
+
 if cd $( dirname $0 ); then :; else
     echo "cd $( dirname $0 ) failed" >&2
     exit 1