diff --git a/grant/license.go b/grant/license.go
index b4dd49b..3889af0 100644
--- a/grant/license.go
+++ b/grant/license.go
@@ -112,6 +112,15 @@ func handleSPDXLicense(license syftPkg.License, licenses []License, licenseLocat
 
 		// we have what seems to be a valid SPDX license ID, let's try and get more info about it
 		spdxLicense, err := spdxlicense.GetLicenseByID(extractedLicense)
+		if err != nil {
+			// The parser returns "<license> WITH <exception>" as a single atom, but the
+			// SPDX license list is indexed by license ID alone, so the lookup above can
+			// only fail for these. Retry with the license the exception applies to; the
+			// full expression is still what ends up on the resulting License.
+			if base, ok := licenseFromExceptionExpression(extractedLicense); ok {
+				spdxLicense, err = spdxlicense.GetLicenseByID(base)
+			}
+		}
 		if err != nil {
 			log.Errorf("unable to get license by ID: %s; no matching spdx id found", extractedLicense)
 			// if we can't find a matching SPDX license, just add the license as-is
@@ -136,6 +145,22 @@ func handleSPDXLicense(license syftPkg.License, licenses []License, licenseLocat
 	return licenses
 }
 
+// licenseFromExceptionExpression returns the license an SPDX "WITH" expression
+// applies to, for example "Apache-2.0" from "Apache-2.0 WITH LLVM-exception".
+func licenseFromExceptionExpression(expression string) (string, bool) {
+	parts := strings.SplitN(expression, " WITH ", 2)
+	if len(parts) != 2 {
+		return "", false
+	}
+
+	license := strings.TrimRight(strings.TrimSpace(parts[0]), "+")
+	if license == "" || strings.TrimSpace(parts[1]) == "" {
+		return "", false
+	}
+
+	return license, true
+}
+
 func addNonSPDXLicense(licenses []License, license syftPkg.License, locations []string) []License {
 	// Filter out sha256: licenses - these are content hashes from Syft when license detection fails
 	if strings.HasPrefix(license.Value, "sha256:") {
diff --git a/grant/license_test.go b/grant/license_test.go
index 949f6d5..585346f 100644
--- a/grant/license_test.go
+++ b/grant/license_test.go
@@ -42,3 +42,54 @@ func TestConvertSyftLicenses_MalformedSPDXExpressionDoesNotPanic(t *testing.T) {
 		})
 	}
 }
+
+// TestConvertSyftLicenses_SPDXExpressionWithException covers SPDX expressions
+// that use the WITH operator. The upstream parser hands these back as a single
+// atom ("Apache-2.0 WITH LLVM-exception"), which is not a key in the SPDX
+// license list, so grant used to log "unable to get license by ID" and fall back
+// to an unresolved license.
+func TestConvertSyftLicenses_SPDXExpressionWithException(t *testing.T) {
+	tests := []struct {
+		expression  string
+		wantSPDX    []string
+		wantLicense []string
+	}{
+		{
+			expression:  "Apache-2.0 WITH LLVM-exception",
+			wantSPDX:    []string{"Apache-2.0 WITH LLVM-exception"},
+			wantLicense: []string{"Apache-2.0"},
+		},
+		{
+			expression:  "GPL-2.0-only WITH Classpath-exception-2.0",
+			wantSPDX:    []string{"GPL-2.0-only WITH Classpath-exception-2.0"},
+			wantLicense: []string{"GPL-2.0-only"},
+		},
+	}
+
+	for _, tt := range tests {
+		tt := tt
+		t.Run(tt.expression, func(t *testing.T) {
+			set := syftPkg.NewLicenseSet(syftPkg.License{Value: tt.expression, SPDXExpression: tt.expression})
+
+			got := ConvertSyftLicenses(set)
+
+			if len(got) != len(tt.wantSPDX) {
+				t.Fatalf("expected %d licenses, got %d", len(tt.wantSPDX), len(got))
+			}
+			for i, want := range tt.wantSPDX {
+				if !got[i].IsSPDX() {
+					t.Fatalf("expected %q to resolve to an SPDX license, got name %q", tt.expression, got[i].Name)
+				}
+				if got[i].SPDXExpression != want {
+					t.Errorf("got SPDX expression %q, want %q", got[i].SPDXExpression, want)
+				}
+				if got[i].LicenseID != tt.wantLicense[i] {
+					t.Errorf("got license id %q, want %q", got[i].LicenseID, tt.wantLicense[i])
+				}
+				if got[i].Name == "" {
+					t.Errorf("expected the license name to be populated from the SPDX list")
+				}
+			}
+		})
+	}
+}