diff --git a/lib/help/key_object.js b/lib/help/key_object.js
index b1d3bcde..c335a697 100644
--- a/lib/help/key_object.js
+++ b/lib/help/key_object.js
@@ -32,6 +32,26 @@ if (!keyObjectSupported) {
 
   const pemToDer = pem => Buffer.from(pem.replace(/(?:-----(?:BEGIN|END)(?: (?:RSA|EC))? (?:PRIVATE|PUBLIC) KEY-----|\s)/g, ''), 'base64')
   const derToPem = (der, label) => `-----BEGIN ${label}-----${EOL}${der.toString('base64').match(/.{1,64}/g).join(EOL)}${EOL}-----END ${label}-----`
+  const unsupported = (label) => {
+    switch (label) {
+      case '1.3.101.110':
+        label = 'X25519'
+        break
+      case '1.3.101.111':
+        label = 'X448'
+        break
+      case '1.3.101.112':
+        label = 'Ed25519'
+        break
+      case '1.3.101.113':
+        label = 'Ed448'
+        break
+      default:
+        label = `OID ${label}`
+    }
+
+    throw new errors.JOSENotSupported(`${label} is not supported in your Node.js runtime version`)
+  }
 
   KeyObject = class KeyObject {
     export ({ cipher, passphrase, type, format } = {}) {
@@ -286,7 +306,8 @@ if (!keyObjectSupported) {
         const parsed = PublicKeyInfo.decode(key, format, { label })
 
         let type, keyObject
-        switch (parsed.algorithm.algorithm.join('.')) {
+        const oid = parsed.algorithm.algorithm.join('.')
+        switch (oid) {
           case '1.2.840.10045.2.1': {
             keyObject = new KeyObject()
             i(keyObject).asn1 = parsed
@@ -302,7 +323,7 @@ if (!keyObjectSupported) {
             break
           }
           default:
-            throw new errors.JOSENotSupported(`OID ${parsed.algorithm.algorithm.join('.')} is not supported in your Node.js runtime version`)
+            unsupported(oid)
         }
 
         return keyObject
@@ -375,7 +396,8 @@ if (!keyObjectSupported) {
         const parsed = PrivateKeyInfo.decode(key, format, { label })
 
         let type, keyObject
-        switch (parsed.algorithm.algorithm.join('.')) {
+        const oid = parsed.algorithm.algorithm.join('.')
+        switch (oid) {
           case '1.2.840.10045.2.1': {
             const OID = asn1.get('OID')
             type = 'sec1'
@@ -388,7 +410,7 @@ if (!keyObjectSupported) {
             break
           }
           default:
-            throw new errors.JOSENotSupported(`OID ${parsed.algorithm.algorithm.join('.')} is not supported in your Node.js runtime version`)
+            unsupported(oid)
         }
 
         i(keyObject).pkcs8 = key
diff --git a/lib/jwk/import.js b/lib/jwk/import.js
index dd195389..78320f61 100644
--- a/lib/jwk/import.js
+++ b/lib/jwk/import.js
@@ -86,7 +86,11 @@ const asKey = (key, parameters, { calculateMissingRSAPrimes = false } = {}) => {
   } else if (key && (typeof key === 'object' || typeof key === 'string')) { // <Object> | <string> | <Buffer> passed to crypto.createPrivateKey or crypto.createPublicKey or <Buffer> passed to crypto.createSecretKey
     try {
       privateKey = createPrivateKey(key)
-    } catch (err) {}
+    } catch (err) {
+      if (err instanceof errors.JOSEError) {
+        throw err
+      }
+    }
 
     try {
       publicKey = createPublicKey(key)
@@ -95,7 +99,11 @@ const asKey = (key, parameters, { calculateMissingRSAPrimes = false } = {}) => {
           x5c: [key.replace(/(?:-----(?:BEGIN|END) CERTIFICATE-----|\s)/g, '')]
         })
       }
-    } catch (err) {}
+    } catch (err) {
+      if (err instanceof errors.JOSEError) {
+        throw err
+      }
+    }
 
     try {
       // this is to filter out invalid PEM keys and certs, i'll rather have them fail import then
diff --git a/test/jwk/import.test.js b/test/jwk/import.test.js
index b08eeaf7..634b3e4b 100644
--- a/test/jwk/import.test.js
+++ b/test/jwk/import.test.js
@@ -165,9 +165,7 @@ test('invalid encoded oct jwk import', async t => {
   }, { instanceOf: errors.JOSEInvalidEncoding, code: 'ERR_JOSE_INVALID_ENCODING', message: 'input is not a valid base64url encoded string' })
 })
 
-if (keyObjectSupported) {
-  test('importing a certificate file populates the certificate properties', t => {
-    const key = asKey(`-----BEGIN CERTIFICATE-----
+const cert = `-----BEGIN CERTIFICATE-----
 MIIC4DCCAcgCCQDO8JBSH914NDANBgkqhkiG9w0BAQsFADAyMQswCQYDVQQGEwJD
 WjEPMA0GA1UEBwwGUHJhZ3VlMRIwEAYDVQQDDAlwa210bHN0d28wHhcNMTkwNjE4
 MTIzMjAxWhcNMjAwNjE3MTIzMjAxWjAyMQswCQYDVQQGEwJDWjEPMA0GA1UEBwwG
@@ -184,9 +182,19 @@ KwwOdRu7VJpAxvweA/3woKl6Cjfy20ZupPH9mxr1R78BMKgEtdFsiLwbB7MOdDbT
 LsrUcEcupXv+gZek22upQKrAk/XFP067KIqKmCEhDidxhP251SloUaruv9cHEx0a
 DKol9eR465FAiBLvg2N7qJHCKlWdn99SgN4Y3kINsuFR7Tj4QIJZNubOjV0YeOgn
 AWzRJlZD89KZAQgjj4Z215QeLxA=
------END CERTIFICATE-----`)
+-----END CERTIFICATE-----`
+
+if (keyObjectSupported) {
+  test('importing a certificate file populates the certificate properties', t => {
+    const key = asKey(cert)
     t.truthy(key.x5c)
     t.truthy(key.x5t)
     t.truthy(key['x5t#S256'])
   })
+} else {
+  test('cannot import a certificate', t => {
+    t.throws(() => {
+      asKey(cert)
+    }, { instanceOf: errors.JOSENotSupported, code: 'ERR_JOSE_NOT_SUPPORTED', message: 'X.509 certificates are not supported in your Node.js runtime version' })
+  })
 }
diff --git a/test/jwk/okp_sig.test.js b/test/jwk/okp_sig.test.js
index 5572610b..889ca0ec 100644
--- a/test/jwk/okp_sig.test.js
+++ b/test/jwk/okp_sig.test.js
@@ -1,12 +1,41 @@
 const test = require('ava')
 
 const { keyObjectSupported } = require('../../lib/help/runtime_support')
+const errors = require('../../lib/errors')
 
-if (!keyObjectSupported) return
+const fixtures = require('../fixtures')
+
+if (!keyObjectSupported) {
+  const JWK = require('../../lib/jwk')
+  ;[
+    [fixtures.PEM.Ed25519.public, 'Ed25519'],
+    [fixtures.PEM.Ed25519.private, 'Ed25519'],
+    [fixtures.PEM.Ed448.public, 'Ed448'],
+    [fixtures.PEM.Ed448.private, 'Ed448'],
+    [fixtures.PEM.X25519.public, 'X25519'],
+    [fixtures.PEM.X25519.private, 'X25519'],
+    [fixtures.PEM.X448.public, 'X448'],
+    [fixtures.PEM.X448.private, 'X448'],
+    [fixtures.JWK.Ed25519, 'Ed25519'],
+    [fixtures.JWK.Ed448, 'Ed448'],
+    [fixtures.JWK.X25519, 'X25519'],
+    [fixtures.JWK.X448, 'X448'],
+    [{ ...fixtures.JWK.Ed25519, d: undefined }, 'Ed25519'],
+    [{ ...fixtures.JWK.Ed448, d: undefined }, 'Ed448'],
+    [{ ...fixtures.JWK.X25519, d: undefined }, 'X25519'],
+    [{ ...fixtures.JWK.X448, d: undefined }, 'X448']
+  ].forEach(([input, label], i, { length }) => {
+    test(`OKP ${i + 1} / ${length}`, t => {
+      t.throws(() => {
+        JWK.asKey(input)
+      }, { instanceOf: errors.JOSENotSupported, code: 'ERR_JOSE_NOT_SUPPORTED', message: `${label} is not supported in your Node.js runtime version` })
+    })
+  })
+  return
+}
 
 const { createPrivateKey, createPublicKey } = require('crypto')
 const { hasProperty, hasNoProperties, hasProperties } = require('../macros')
-const fixtures = require('../fixtures')
 
 const OKPKey = require('../../lib/jwk/key/okp')