diff --git a/NEWS.md b/NEWS.md
index e54201ab67..ad081b7e9c 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -5,6 +5,13 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [0.9.9] – 2023-12-14
+
+### Fixed
+
+* introduced a nonzero `atol` for all point and vector checks that compre to zero.
+  This makes those checks a bit more relaxed by default and resolves [#630](https://github.com/JuliaManifolds/Manifolds.jl/issues/630).
+
 ## [0.9.8] - 2023-11-17
 
 ### Fixed
diff --git a/Project.toml b/Project.toml
index 490fd5c2bf..0bd91a22b8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Manifolds"
 uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 authors = ["Seth Axen <seth.axen@gmail.com>", "Mateusz Baran <mateuszbaran89@gmail.com>", "Ronny Bergmann <manopt@ronnybergmann.net>", "Antoine Levitt <antoine.levitt@gmail.com>"]
-version = "0.9.8"
+version = "0.9.9"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
diff --git a/src/manifolds/SymplecticStiefel.jl b/src/manifolds/SymplecticStiefel.jl
index 455f8c1aef..a43c064e4b 100644
--- a/src/manifolds/SymplecticStiefel.jl
+++ b/src/manifolds/SymplecticStiefel.jl
@@ -148,16 +148,16 @@ The tolerance can be set with `kwargs...` (e.g. `atol = 1.0e-14`).
 check_vector(::SymplecticStiefel, ::Any...)
 
 function check_vector(
-    M::SymplecticStiefel,
+    M::SymplecticStiefel{S,𝔽},
     p,
     X::T;
     atol=sqrt(prod(representation_size(M))) * eps(real(float(number_eltype(T)))),
     kwargs...,
-) where {T}
+) where {S,T,𝔽}
     n, k = get_parameter(M.size)
     # From Bendokat-Zimmermann: T_pSpSt(2n, 2k) = \{p*H | H^{+} = -H  \}
     H = inv(M, p) * X  # ∈ ℝ^{2k × 2k}, should be Hamiltonian.
-    H_star = inv(Symplectic(2k, field), H)
+    H_star = inv(Symplectic(2k, 𝔽), H)
     hamiltonian_identity_norm = norm(H + H_star)
 
     if !isapprox(hamiltonian_identity_norm, 0; atol=atol, kwargs...)