diff --git a/.github/workflows/main.yaml b/.github/workflows/main.yaml
index 95b0962b0..541c99c82 100644
--- a/.github/workflows/main.yaml
+++ b/.github/workflows/main.yaml
@@ -195,6 +195,25 @@ jobs:
       run: ./ci/update-musl.sh
     - run: cargo clippy --workspace --all-targets
 
+  build-custom:
+    name: Build custom target
+    runs-on: ubuntu-24.04
+    timeout-minutes: 10
+    steps:
+    - uses: actions/checkout@v4
+    - name: Install Rust
+      run: |
+        rustup update nightly --no-self-update
+        rustup default nightly
+        rustup component add rust-src
+    - uses: Swatinem/rust-cache@v2
+    - run: |
+        # Ensure we can build with custom target.json files (these can interact
+        # poorly with build scripts)
+        cargo build -p compiler_builtins -p libm \
+          --target etc/thumbv7em-none-eabi-renamed.json \
+          -Zbuild-std=core
+
   benchmarks:
     name: Benchmarks
     timeout-minutes: 20
@@ -331,6 +350,7 @@ jobs:
   success:
     needs:
       - benchmarks
+      - build-custom
       - clippy
       - extensive
       - miri
diff --git a/compiler-builtins/configure.rs b/compiler-builtins/configure.rs
index a1e45080e..9721ddf09 100644
--- a/compiler-builtins/configure.rs
+++ b/compiler-builtins/configure.rs
@@ -45,9 +45,16 @@ impl Target {
         let out = cmd
             .output()
             .unwrap_or_else(|e| panic!("failed to run `{cmd:?}`: {e}"));
-        assert!(out.status.success(), "failed to run `{cmd:?}`");
         let rustc_cfg = str::from_utf8(&out.stdout).unwrap();
 
+        // If we couldn't query `rustc` (e.g. a custom JSON target was used), make the safe
+        // choice and leave `f16` and `f128` disabled.
+        let rustc_output_ok = out.status.success();
+        let reliable_f128 =
+            rustc_output_ok && rustc_cfg.lines().any(|l| l == "target_has_reliable_f128");
+        let reliable_f16 =
+            rustc_output_ok && rustc_cfg.lines().any(|l| l == "target_has_reliable_f16");
+
         Self {
             triple,
             triple_split,
@@ -67,8 +74,8 @@ impl Target {
                 .split(",")
                 .map(ToOwned::to_owned)
                 .collect(),
-            reliable_f128: rustc_cfg.lines().any(|l| l == "target_has_reliable_f128"),
-            reliable_f16: rustc_cfg.lines().any(|l| l == "target_has_reliable_f16"),
+            reliable_f128,
+            reliable_f16,
         }
     }
 
diff --git a/etc/thumbv7em-none-eabi-renamed.json b/etc/thumbv7em-none-eabi-renamed.json
new file mode 100644
index 000000000..81273d44e
--- /dev/null
+++ b/etc/thumbv7em-none-eabi-renamed.json
@@ -0,0 +1,23 @@
+{
+  "abi": "eabi",
+  "arch": "arm",
+  "c-enum-min-bits": 8,
+  "crt-objects-fallback": "false",
+  "data-layout": "e-m:e-p:32:32-Fi8-i64:64-v128:64:128-a:0:32-n32-S64",
+  "emit-debug-gdb-scripts": false,
+  "frame-pointer": "always",
+  "linker": "rust-lld",
+  "linker-flavor": "gnu-lld",
+  "llvm-floatabi": "soft",
+  "llvm-target": "thumbv7em-none-eabi",
+  "max-atomic-width": 32,
+  "metadata": {
+    "description": "Bare ARMv7E-M",
+    "host_tools": false,
+    "std": false,
+    "tier": 2
+  },
+  "panic-strategy": "abort",
+  "relocation-model": "static",
+  "target-pointer-width": "32"
+}
diff --git a/libm/configure.rs b/libm/configure.rs
index 6562ecbe5..f9100d2d5 100644
--- a/libm/configure.rs
+++ b/libm/configure.rs
@@ -43,9 +43,16 @@ impl Config {
         let out = cmd
             .output()
             .unwrap_or_else(|e| panic!("failed to run `{cmd:?}`: {e}"));
-        assert!(out.status.success(), "failed to run `{cmd:?}`");
         let rustc_cfg = str::from_utf8(&out.stdout).unwrap();
 
+        // If we couldn't query `rustc` (e.g. a custom JSON target was used), make the safe
+        // choice and leave `f16` and `f128` disabled.
+        let rustc_output_ok = out.status.success();
+        let reliable_f128 =
+            rustc_output_ok && rustc_cfg.lines().any(|l| l == "target_has_reliable_f128");
+        let reliable_f16 =
+            rustc_output_ok && rustc_cfg.lines().any(|l| l == "target_has_reliable_f16");
+
         Self {
             target_triple,
             manifest_dir: PathBuf::from(env::var("CARGO_MANIFEST_DIR").unwrap()),
@@ -59,8 +66,8 @@ impl Config {
             target_string: env::var("TARGET").unwrap(),
             target_vendor: env::var("CARGO_CFG_TARGET_VENDOR").unwrap(),
             target_features,
-            reliable_f128: rustc_cfg.lines().any(|l| l == "target_has_reliable_f128"),
-            reliable_f16: rustc_cfg.lines().any(|l| l == "target_has_reliable_f16"),
+            reliable_f128,
+            reliable_f16,
         }
     }
 }