diff --git a/src/MOI/MOI_wrapper.jl b/src/MOI/MOI_wrapper.jl
index 135d73f6..9ad4a2c0 100644
--- a/src/MOI/MOI_wrapper.jl
+++ b/src/MOI/MOI_wrapper.jl
@@ -2787,15 +2787,63 @@ function MOI.get(
     return _dual_multiplier(model) * p[]
 end
 
-# function MOI.get(
-#     model::Optimizer, attr::MOI.ConstraintDual,
-#     c::MOI.ConstraintIndex{MOI.ScalarQuadraticFunction{Float64}, <:Any}
-# )
-#     _throw_if_optimize_in_progress(model, attr)
-#     MOI.check_result_index_bounds(model, attr)
-#     pi = model.cached_solution.quadratic_dual[_info(model, c).row]
-#     return _dual_multiplier(model) * pi
-# end
+function MOI.get(
+    model::Optimizer,
+    attr::MOI.ConstraintDual,
+    c::MOI.ConstraintIndex{MOI.ScalarQuadraticFunction{Float64}, <:Any},
+)
+    # For more information on QCP duals, see
+    # https://www.ibm.com/support/knowledgecenter/SSSA5P_12.10.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/cont_optim/qcp/17_QCP_duals.html
+    _throw_if_optimize_in_progress(model, attr)
+    MOI.check_result_index_bounds(model, attr)
+    # The derivative of a quadratic f(x) = x^TQx + a^Tx + b <= 0 is
+    # ∇f(x) = Q^Tx + Qx + a
+    # The dual is undefined if x is at the point of the cone. This can only be
+    # checked to numeric tolerances. We use `cone_top_tol`.
+    cone_top, cone_top_tol = true, 1e-6
+    x = zeros(length(model.variable_info))
+    ret = CPXgetx(model.env, model.lp, x, 0, length(x) - 1)
+    _check_ret(model, ret)
+    ∇f = zeros(length(x))
+    a_i, a_v, qrow, qcol, qval = _CPXgetqconstr(model, c)
+    for (i, j, v) in zip(qrow, qcol, qval)
+        ∇f[i + 1] += v * x[j + 1]
+        ∇f[j + 1] += v * x[i + 1]
+        if abs(x[i + 1]) > cone_top_tol || abs(x[j + 1]) > cone_top_tol
+            cone_top = false
+        end
+    end
+    for (i, v) in zip(a_i, a_v)
+        ∇f[i + 1] += v
+        if abs(x[i + 1]) > cone_top_tol
+            cone_top = false
+        end
+    end
+    # TODO(odow): if at top of cone (x = 0) dual multiplier is ill-formed.
+    if cone_top
+        return NaN
+    end
+    qind = Cint(_info(model, c).row - 1)
+    nz_p, surplus_p = Ref{Cint}(), Ref{Cint}()
+    CPXgetqconstrdslack(
+        model.env, model.lp, qind, nz_p, C_NULL, C_NULL, 0, surplus_p
+    )
+    ind = Vector{Cint}(undef, -surplus_p[])
+    val = Vector{Cdouble}(undef, -surplus_p[])
+    ret = CPXgetqconstrdslack(
+        model.env, model.lp, qind, nz_p, ind, val, -surplus_p[], surplus_p
+    )
+    _check_ret(model, ret)
+    ∇f_max, ∇f_i = findmax(abs.(∇f))
+    if ∇f_max > cone_top_tol
+        for (i, v) in zip(ind, val)
+            if i + 1 == ∇f_i
+                return _dual_multiplier(model) * v / ∇f[∇f_i]
+            end
+        end
+    end
+    return 0.0
+end
 
 function MOI.get(model::Optimizer, attr::MOI.ObjectiveValue)
     _throw_if_optimize_in_progress(model, attr)
@@ -3464,3 +3512,27 @@ function MOI.set(
     return
 end
 
+function MOI.get(
+    model::Optimizer,
+    ::MOI.ConstraintDual,
+    c::MOI.ConstraintIndex{MOI.VectorOfVariables, MOI.SecondOrderCone},
+)
+    f = MOI.get(model, MOI.ConstraintFunction(), c)
+    qind = Cint(_info(model, c).row - 1)
+    surplus_p = Ref{Cint}()
+    CPXgetqconstrdslack(
+        model.env, model.lp, qind, C_NULL, C_NULL, C_NULL, 0, surplus_p
+    )
+    ind = Vector{Cint}(undef, -surplus_p[])
+    val = Vector{Cdouble}(undef, -surplus_p[])
+    ret = CPXgetqconstrdslack(
+        model.env, model.lp, qind, C_NULL, ind, val, -surplus_p[], surplus_p
+    )
+    _check_ret(model, ret)
+    slack = zeros(length(model.variable_info))
+    for (i, v) in zip(ind, val)
+        slack[i + 1] += v
+    end
+    z = _dual_multiplier(model)
+    return [z * slack[_info(model, v).column] for v in f.variables]
+end
diff --git a/test/MathOptInterface/MOI_wrapper.jl b/test/MathOptInterface/MOI_wrapper.jl
index b15416ba..3f8c5635 100644
--- a/test/MathOptInterface/MOI_wrapper.jl
+++ b/test/MathOptInterface/MOI_wrapper.jl
@@ -12,14 +12,11 @@ const CONFIG = MOIT.TestConfig()
 
 const OPTIMIZER = CPLEX.Optimizer()
 MOI.set(OPTIMIZER, MOI.Silent(), true)
-const BRIDGED_OPTIMIZER = MOI.Bridges.full_bridge_optimizer(OPTIMIZER, Float64)
+# Turn off presolve reductions so CPLEX will generate infeasibility
+# certificates.
+MOI.set(OPTIMIZER, MOI.RawParameter("CPX_PARAM_REDUCE"), 0)
 
-const CERTIFICATE_OPTIMIZER = CPLEX.Optimizer()
-MOI.set(CERTIFICATE_OPTIMIZER, MOI.Silent(), true)
-MOI.set(CERTIFICATE_OPTIMIZER, MOI.RawParameter("CPX_PARAM_REDUCE"), 0)
-MOI.set(CERTIFICATE_OPTIMIZER, MOI.RawParameter("CPX_PARAM_PRELINEAR"), 0)
-const BRIDGED_CERTIFICATE_OPTIMIZER =
-    MOI.Bridges.full_bridge_optimizer(CERTIFICATE_OPTIMIZER, Float64)
+const BRIDGED_OPTIMIZER = MOI.Bridges.full_bridge_optimizer(OPTIMIZER, Float64)
 
 function test_basic_constraint_tests()
     MOIT.basic_constraint_tests(BRIDGED_OPTIMIZER, CONFIG; exclude = [
@@ -62,12 +59,7 @@ function test_unittest()
         # TODO(odow): bug! We can't delete a vector of variables  if one is in
         # a second order cone.
         "delete_soc_variables",
-
-        # CPLEX returns INFEASIBLE_OR_UNBOUNDED without extra parameters.
-        # See below for the test.
-        "solve_unbounded_model",
     ])
-    MOIT.solve_unbounded_model(CERTIFICATE_OPTIMIZER, CONFIG)
 end
 
 function test_modificationtest()
@@ -76,18 +68,11 @@ end
 
 function test_contlineartest()
     MOIT.contlineartest(BRIDGED_OPTIMIZER, CONFIG, [
-        # These tests require extra parameters to be set.
-        "linear8a", "linear8b", "linear8c",
-
         # TODO(odow): This test requests the infeasibility certificate of a
         # variable bound.
         "linear12"
     ])
 
-    MOIT.linear8atest(CERTIFICATE_OPTIMIZER, CONFIG)
-    MOIT.linear8btest(CERTIFICATE_OPTIMIZER, CONFIG)
-    MOIT.linear8ctest(CERTIFICATE_OPTIMIZER, CONFIG)
-
     MOIT.linear12test(OPTIMIZER, MOIT.TestConfig(infeas_certificates=false))
 end
 
@@ -101,35 +86,34 @@ end
 
 function test_contquadratictest()
     MOIT.contquadratictest(
-        BRIDGED_CERTIFICATE_OPTIMIZER,
-        # TODO(odow): duals for quadratic problems.
-        MOIT.TestConfig(duals = false, atol = 1e-3, rtol = 1e-3),
+        BRIDGED_OPTIMIZER,
+        MOIT.TestConfig(atol = 1e-3, rtol = 1e-3),
         ["ncqcp"], # CPLEX doesn't support non-convex problems
     )
 end
 
 function test_contconic()
-    MOIT.lintest(BRIDGED_OPTIMIZER, CONFIG, [
-        # These tests require extra parameters to be set.
-        "lin3", "lin4"
-    ])
-
-    MOIT.lin3test(BRIDGED_CERTIFICATE_OPTIMIZER, CONFIG)
-    MOIT.lin4test(BRIDGED_CERTIFICATE_OPTIMIZER, CONFIG)
-
-    # TODO(odow): duals for SOC constraints.
-    soc_config = MOIT.TestConfig(duals = false, atol=5e-3)
+    MOIT.lintest(BRIDGED_OPTIMIZER, CONFIG)
 
-    MOIT.soctest(BRIDGED_OPTIMIZER, soc_config, [
-        "soc3"
-    ])
+    soc_config = MOIT.TestConfig(atol=5e-3)
 
+    # TODO(odow): investigate why infeasibility certificates not generated for
+    # SOC.
+    MOIT.soctest(BRIDGED_OPTIMIZER, soc_config, ["soc3"])
     MOIT.soc3test(
         BRIDGED_OPTIMIZER,
-        MOIT.TestConfig(duals = false, infeas_certificates = false, atol = 1e-3)
+        MOIT.TestConfig(atol = 1e-3, infeas_certificates = false)
     )
 
-    MOIT.rsoctest(BRIDGED_OPTIMIZER, soc_config)
+    MOIT.rsoctest(BRIDGED_OPTIMIZER, soc_config, ["rotatedsoc2"])
+    MOIT.rotatedsoc2test(
+        BRIDGED_OPTIMIZER,
+        # Need for `duals = false` fixed by https://github.com/jump-dev/MathOptInterface.jl/pull/1171
+        # Remove in a future MOI 0.9.18+ release.
+        MOIT.TestConfig(
+            atol = 1e-3, infeas_certificates = false, duals = false
+        ),
+    )
 
     MOIT.geomeantest(BRIDGED_OPTIMIZER, soc_config)
 end