diff --git a/src/script/sign.h b/src/script/sign.h
--- a/src/script/sign.h
+++ b/src/script/sign.h
@@ -698,4 +698,12 @@
                                   unsigned int nIn, const CTxOut &txout);
 void UpdateInput(CTxIn &input, const SignatureData &data);
 
+/**
+ * Check whether we know how to sign for an output like this, assuming we have
+ * all private keys. While this function does not need private keys, the passed
+ * keystore is used to look up public keys and redeemscripts by hash.
+ * Solvability is unrelated to whether we consider this output to be ours.
+ */
+bool IsSolvable(const SigningProvider &provider, const CScript &script);
+
 #endif // BITCOIN_SCRIPT_SIGN_H
diff --git a/src/script/sign.cpp b/src/script/sign.cpp
--- a/src/script/sign.cpp
+++ b/src/script/sign.cpp
@@ -621,3 +621,20 @@
     ret.keys.insert(b.keys.begin(), b.keys.end());
     return ret;
 }
+
+bool IsSolvable(const SigningProvider &provider, const CScript &script) {
+    // This check is to make sure that the script we created can actually be
+    // solved for and signed by us if we were to have the private keys. This is
+    // just to make sure that the script is valid and that, if found in a
+    // transaction, we would still accept and relay that transaction.
+    SignatureData sigs;
+    if (ProduceSignature(provider, DUMMY_SIGNATURE_CREATOR, script, sigs)) {
+        // VerifyScript check is just defensive, and should never fail.
+        bool verified =
+            VerifyScript(sigs.scriptSig, script, STANDARD_SCRIPT_VERIFY_FLAGS,
+                         DUMMY_CHECKER);
+        assert(verified);
+        return true;
+    }
+    return false;
+}
diff --git a/src/test/descriptor_tests.cpp b/src/test/descriptor_tests.cpp
--- a/src/test/descriptor_tests.cpp
+++ b/src/test/descriptor_tests.cpp
@@ -30,7 +30,7 @@
 // Derivation needs access to private keys
 constexpr int HARDENED = 2;
 // This descriptor is not expected to be solvable
-// constexpr int UNSOLVABLE = 4;
+constexpr int UNSOLVABLE = 4;
 // We can sign with this descriptor (this is not true when actual BIP32
 // derivation is used, as that's not integrated in our signing code)
 constexpr int SIGNABLE = 8;
@@ -103,6 +103,9 @@
             for (size_t n = 0; n < spks.size(); ++n) {
                 BOOST_CHECK_EQUAL(ref[n],
                                   HexStr(spks[n].begin(), spks[n].end()));
+                BOOST_CHECK_EQUAL(
+                    IsSolvable(Merge(key_provider, script_provider), spks[n]),
+                    (flags & UNSOLVABLE) == 0);
 
                 if (flags & SIGNABLE) {
                     CMutableTransaction spend;